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THE UNIVERSITY 
OF ILLINOIS 
LIBRARY 


The 
Frank Hall collection 
of arithmetics, 
presented by Professor 
H. L. Rietz of the | 
University of Iowa. | 


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MANUAL 


OF 


INTELLECTUAL ARITHMETIC: 


AN INDEPENDENT TREATISE UPON THE 
BASIS OF MENTAL ARITHMETIC, 


BY 


AU WvuUinyp Ut AJ 


Greenleat , BENJAMIN oy Its Leen A. M., 


AUTHOR OF A MATHEMATICAL SERIES. 


BOSTON: 

PUBLISHED BY ROBERT S. DAVIS & CO. 
PHILADELPHIA: KEYSTONE SCHOOL AND CHURCH FURNITURE CO. 
NEW YORK: BAKER, PRATT, & COMPANY, 19 BOND ‘STREET. 
CHICAGO: JANSEN, MCCLURG, & COMPANY. 

DUBUQUE: GROSVENOR & HARGER. 


GREENLEAF’S 


MATHEMATICAL SERIES. 


A COMPLETE COURSE, ANALYTICAL, PRACTICAL, PROGRESSIVE, 
AND SCIENTIFIC. 


Wew Primary Arithmetic, New Elementary Algebra, 
New Elementary Arithmetic, New Higher Algebra, 
New Practical Arithmetic, Elements of Geometry, 


Geometry and Trigonometry. 


MANUAL OF INTELLECTUAL ARITHMETIC. 


SHORTER COURSE IN GEOMETRY. 
ELEMENTS OF PLANE AND SPHERICAL TRIGONOMETRY. 


Copyricut, 1877, 
‘By HENRY B. MAGLATHLIN. 


RIVERSIDE, CAMBRIDGE : 
ELECTROTYPED AND PRINTED BY 
H. QO. HOUGHTON AND COMPANY. 


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& G4. nev, MATHEMATICS LIBRARY 


INTRODUCTION. 


RAL exercises in numbers of an inductive nature, . 

in the estimation of sound educators, have a 

peculiar power in strengthening and maturing the 
mind. | 

The appreciation of mental arithmetic as a means 

of education has given rise to urgent demands for 


improved methods of teaching the science. 


To meet in a degree new educational wants, this 
manual, based upon the works of Benjamin Green- 
leaf, has been prepared. Its lessons recognize the 
normal growth of the reasoning powers. The aim 
throughout has been to make the subject treated 
attractive and interesting ; and by easy steps to ad- 
vance the learner by sure progress. 


Some pages of slate or blackboard work have been 
appended. ‘These may be used in supplementing the 
oral exercises of the text, and the same form of solu- 
tion be shown to apply alike to mental and written 
problems. 


In the preparation of the present edition of this 
book, credit is due to J. V. Jackman for testing the 
copy in the schoolroom and for many valuable sug- 


gestions. 464249 


TO TEACHERS. 


THE extent to which the book can be dispensed 
with by the class, in recitation, should be determined 
by the nature of the lesson and the attainment of the 
pupil. 

When the book is not used, each question should 
be repeated by the pupil after the teacher, and the 
required solution should always be given promptly, 
and in every case should form a complete sentence. 

A brief form of analysis only is given in the book, | 
so as to allow the fullest scope for the exercise of in- 
genuity, judgment, and discrimination on the part of 
the pupil in the invention of others. 

No form of solution, however, should be permitted 
to pass, unless it is neatly expressed, and is entirely 
accurate. 

Each example can be taken as a model for many 
original examples to be dictated by the teacher. In 
no other way than by giving a multiplicity of ex- 
amples, can a teacher fix firmly in the minds of his 
pupils the principles which he is imparting. 

Mental and written arithmetic should always be 
combined. Hence the wise teacher will always fol- 
low up what the pupil has learned, with suitable ex- 
amples, illustrating the same principles, which will 
require the use of pencil or crayon. 


INTELLECTUAL ARITHMETIC. 


hy |! 
ey eal 


Age 
“i 
* 


NUMBERS. 


LESSON I. 


1. 1. Count ten. How many ones in ten? 
2. Count twenty, or two tens. How many ones in 
two tens? In twenty? 
8. Count thirty. How many tens have you 
counted ? How many ones in three tens? In thirty? 
% 


Can NUMBERS. 


4. Count forty. How many ones in four tens? 
In forty ? 

5. Count fifty. How many ones in five tens? In 
fifty ? 

6. How many ones in six tens? In seven tens? 
In eight tens? In nine tens? In ten tens? 

7. How many tens in sixty? In seventy? In 
eighty ? In ninety ? 

8. How many are ten and one? ‘Ten and two? 
Ten and three? Ten and five? Ten and nine? 

9. How many tens and ones are there in twelve ? 
In fifteen ? In nineteen ? 

10. How many are two tens and one? ‘Two tens 
and two? ‘Two tens and four? ‘Two tens and six ?- 
Two tens and eight ? - 

11. How many tens and ones are there in twenty- 
one? In twenty-two? In twenty-five? In twenty- 
nine ? . 

12. How many are expressed by 1?° By 2? By 
3? By 4? By5? By6? ByT? By 8? By 9? 

13. How many tens are expressed by 10? By 20? 
By 80? By 40? By 50? By 60? By 70? By 
80? By 90? 

14. How many ones are expressed by 11? By 15? 
By 19? By 21? By 23? By 42? By 57? 

15. How many tens and ones are expressed by 18 ? 
By 28? By 63? By 75? By 98? 

16. How many tens are expressed by 100? By 
200? By 400? By 700? By 800? 

17. How many hundreds and tens are expressed 
by 110? By 210? By 220? By 350? By 480? 
Bv 970? | . 


ADDITION. a 


18. How many hundreds, tens, and ones are ex- 
pressed by 111? By 222? By 561? By 163? 
By 887 ? 

DEFINITIONS. 
2. What isaunit? A Unit is a single thing, or 
one. : 

oo. Whatisanumber? A Number is a unit or 
a collection of units. 


ADDITION. 


—_oe— 


LESSON II. 


4, 1. John had 1 peach and his father gave him 
another ; how many peaches did he then have ? 

SoLution. — John had 1 peach and his father gave him an- 
other ; he then had 1 peach and 1 peach, or 2 peaches. 

2. Susan has 2 books, and Mary has 1 book ; how 
many books have they both? 

3. If you had 2 cherries, and I should give you 2, 
how many cherries would you then have ? 

4. Lucy found 2 pins, and Sarah found 3 pins; 
how many did they both find ? 

5. If you should recite 2 lessons to-day, and 4 to- 
morrow, how many would you recite in all ? 

6. A lemon cost 2 cents, and an orange cost 5 
cents; how many cents did both cost ? 

7. Gave 2 cents for a pencil, and 6 cents for some 
paper; what was the cost of both ? 

8. On one bush there are 2 roses, and on another 
there are 7 roses; how many on both bushes ? 


8 ADDITION. 


9. 2 boys and 8 boys are how many boys ? 

10. A farmer sold a lamb for 2 dollars, and a calf 
for 9 dollars; how many dollars did he get for 
both ? 

11. Alfred caught 3 birds, and Jason caer 1 bird ; 
how many birds did they both catch ? 

12. James has 3 marbles, and Charles has 2 mar- 
bles ; how many marbles have they both? 

13. A man sold a pig for 3.dollars, and a sheep for 
8 dollars; how many dollars did he receive for both ? 

14. Mary has 3 books, and Margaret has 4 books ; 
how many books have they both? 

15. Edward gave 3 cents for a postage-stamp, and 
5 cents for a box of wafers; how much did both 
cost ? 

16. Eliza is 8 years old; Hon old will she be in 6 
years, if she lives? 

17. A farmer has 3 cows in one field, and 7 in an- 
other ; how many has he in both ? 

18. In aclass there are 3 girls and 8 boys; how 
many pupils are there in the class? 

19. A boy found under one apple-tree 3 apples, 
and under another 9 apples; how many did he find in 
all ? 

20. If you have 4 chestnuts in one hand, and 1 
chestnut in the other, how many have you in both 
hands ? 

21. Susan had 4 merit marks, and obtained 2 more; - 
how many did she then have ? 

22. George found 4 eggs in one nest, and 8 eggs in 
another ; how many did he find in both ? 


ADDITION. 9 


23. A man bought a cord of wood for 4 dollars, 
and half a ton of coal for 4 dollars; how much did 
both cost him ? 

24. A lady paid 4 cents for a skein of silk, and 5 


- . cents for a spool of cotton; how much did she pay 


for both ? 
25. Ella gave 4 cents for candy, and 6 cents for 
nuts; how much did she give for both ? 


) DEFINITIONS. 
5. What is the sum of two or more numbers? The 
Sem of two or more numbers is that number which 
is equal to those numbers. 
6. What is addition? Addition is the process 
of finding a number equal to two or more given num- 
bers of the same kind. 


LESSON ILL. 


1. 1 and 1 are how many ? 
. 2 and 1 are how many? 
2 and 5 are how many ? 
. 2 and 3 are how many? 
. 2and 7 are how many ? 
. 2 and 2 are how many? 
. 2 and 6 are how many ? 
. 2 and 4 are how many ? 
. 2 and 8 are how many ? 
10. 2 and 10 are how many ? 
11. 3 and 8 are how many ? 
12. 3 and 6 are how many ? 
13. 8 and 5 are how many ? 


OMAmNp wD ek 


10 ADDITION. 


14. 3 and 4 are how many ? 

15. 3 and 7 are how many ? 

16. 3 and 9 are how many? 

17. 8 and 8 are how many ? 

18. 4 and 8 are how many ? 

19. 4 and 6 are how many ? 

20. 4 and 5 are how many ? 

21. 4 and 7 are how many ? 

22. 4 and 4 are how many? 

23. 4 and 9 are how many ? 

24. Abby found 5 pins, and Jane found 1; how 
many did they both find ? 

25. Ellen had 5 chickens, and her father gave her 
2; how many did she then have ? 

26. Mary gave 5 cents for tape, and 3 cents for 
thread ; how much did she give for both ? 

27. George bought 5 marbles, and had 4 given 
him; how many did lie then have? 

28. John gave to one schoolmate 5 nuts, and to 
another the same number ; how many did he give to 
both ? 

29. Olive had 5 pins on her cushion, and stuck on 
it 6; how many did she then have? 

30. If you spend 5 cents, and have 7 cents left, | 
how many had you at first ? 

31. 5 oranges and 8 oranges are how many or- 
anges ? 

32. Joseph, having lost 5 cents, had only 9 cents 
left ; how many had he at first ? 

33. Gave 6 cents for paper, and 1 cent for a pen; 
how much did both cost ? 


ADDITION. 11 


34, If you had 6 apples, and should have 2 given 
you, how many would you then have ? 

30. How many slates are 6 slates and 3 slates ? 

36. Gave 6 cents for paper, and 4 cents for quills ; 
how many cents were paid for both ? 

37. If you should give 6 dollars for a vest, and 5 
dollars for a pair of boots, how much would both 
cost ? 

38. A bookseller sold in one day 6 books, and in 
another day 6 ; how many did he sell in all ? 

39. A farmer sold 6 sheep, and retained 7; how 
many had he at first ? 

40. If a clock cost 6 dollars, and a table 8 dollars 
what would be the cost of both ? 

41. A farmer has 6 cows in one pasture, and 9 in 
another ; how many has he in both ? 

42. Paid 7 cents for a ruler, and 1 cent for a pen- 
cil; what did both cost? 

43. If a paper of pins cost 7 cents, and a pencil 2 
cents, how many cents must be paid for both? 

44. If 7 birds are upon a gate, and 3 upon the 
ground, how many are there in all ? 

45. T books and 4 books are how many books ? 

46. 7 horses and 5 horses are how many horses ? 

47. Laura had 7 needles, and her sister gave her 
6; how many did she then have ? 

48. How many cents are 8 cents and 7 cents ? 

49. John has 8 books and Edwin 9; how many 
have both ? 

50. William had 9 dollars and his father gave him 
9; how many did he then have ? 


12 ADDITION. 


LESSON IV. 


8. 1. 5 and 5 are how many? 
2. 5 and 8 are how many ? 
3. 5 and 7 are how many ? 
4. 5 and 6 are how many ? 
5. 5 and 9 are how many ? 
6. 6 and 6 are how many ? 
7. 6 and 9 are how many ? 
8. 6 and 8 are how many ? 
9. 6 and 7 are how many ? 

10. 7 and 8 are how many ? 

11. 7 and 8 are how many ? 

12. 7 and 2 are how many ? 

13. 5 and 4 are how many ? 

14. 7 and 1 are how many ? 

15. 1 and 9 are how many ? 

16. 6 and 4 are how many ? 

17. William bought 7 marbles, and had 7 given 
him ; how many did he then have ? 

18. If Charles has two notes due him, one for 7 
dollars, and the other for 8 dollars, how much is due 
him in all ? 

19. There are on one side of a room 7 chairs, and 
on the other side 9; how many are there on both 
sides ? 

20. John had 8 cents, and his father gave him 1; 
how many cents did he then have ? 

21. James is 8 years old; how old will he be if he 
lives 2 years longer ? 

22, Paid 8 dollars for sugar, and 8 dollars for salt; 
how much was paid for both ? 


ADDITION. 13 


23. In a certain class there are 8 boys, and 4 girls ; 
how many scholars are there in the class ? 

24. Gave 8 dollars for wood, and 5 dollars for coal ; 
how much did both cost ? 

25. If a coat cost 8 dollars, and a vest 6 dollars, 
how much will both cost ? 

26. If you had 8 dollars, and your father should 
give you 7, how many would you have? 

27. If a barrel of flour cost 8 dollars, and half a 
barrel of beef cost 8 dollars, how much will both 
cost? 

28. Bought a hundred weight of sugar for 8 dol- 
lars, and a quantity of butter for 9 dollars; what 
did the whole cost ? 

29. Levi earned in one week 9 dollars, and in an- 
other week only 1 dollar; how much did he earn in 
all ? ; 

830. Paid 9 dollars for a saddle, and 2 dollars for a 
bridle ; how much did both cost ? 

31. Andrew paid 9 cents for a quart of nuts, and 
3 cents for candy; how much did the whole cost 
him ? 

32. James raised 9 melons, and his brother raised 
4; how many did they both raise ? 

33. If you should have 9°pens given you of one 
kind, and 6 of another kind, how many pens would 
you then have ? . 

34. Edward walked 9 miles in one day, and 7 
miles the next day ; how many miles did he walk in 
all ? 

35. A farmer sold 9 pounds of butter at one time, 


14 | ADDITION. 


and 8 pounds at another ; how many pounds did he 
sell in all ? 

36. A miller ground 9 bushels of wheat, and 9 
bushels of corn; how many bushels did he grind in 
all ? 


LESSON V. 


9. 1. John has 3 marbles, Samuel 5, and Jacob 
4; how many have they all? 

Sotution. — They all have the sum of 3 marbles, 5 marbles, and 4 
marbles, which is 12 marbles. 

2. Gave 3 cents to Susan, 4 to Emily, and 2 to 
Ann; how many cents were given to them all ? 

3. Gave 4 nuts to one boy, 2 to another, and 4 
to another; how many nuts were given to the three 
boys ? 

4, Bought a-pound of sugar for 9 cents, a pound 
of raisins for 7 cents, and an ounce of nutmegs for 
6 cents ; what was the cost of the whole? 

5. James is 4 years old, Edward 6, and Charles 
8; what is the sum of their ages ? 

6. Bought a sheep for 9 dollars, a lamp for 2 dollars, 
and a pig for 5 dollars; what did the whole cost ? 

7. Paid for wood 7 dollars, for coal 6 dollars, and 
for a saw 2 dollars ; how much did the whole cost ? 

8. Charles had 3 peaches, and received 3 more 
from Albert, and 2 more from Edmund; how many ~ 
did he then have ? 

9. A farmer sold 5 bushels of wheat, 7 bushels of 
rye, and 8 bushels of corn ; how many bushels did he 
sell ? 


ADDITION. 15 


10. A lady expended for silk 4 dollars, for gloves 
1 dollar, and for a bonnet 9 dollars ; how many dol- 
lars did she expend in all ? 

11. Bought a barrel of flour for 6 dollars, a bar- 
rel of apples for 3 dollars, and a keg of molasses for 
8 dollars; what was the cost of the whole? 

12. John spends 9 cents for paper, 3 cents for 
wafers, and 5 cents for pens; how many cents does 
he spend in all ? 

13. George buys 6 oranges at one time, 2 at 
another, and 8 at another; how many oranges does 
he buy in all? 

14. 5 dollars, 9 dollars, and 4 dollars are how 
many dollars ? 

15. How many are 1, 7, and 6? 3, 5,and 4? 3, 
4,and2? 4, 5, and 6? 

16. Susan has 3 birds, Abby 4, and Ellen 9; how 
many have they all? 3,4, and 9 are how many ? 

17. How many pigeons are 10 pigeons and 2 
pigeons ?. 10 pigeons and 5 pigeons? 10 pigeons 
and 4 pigeons ? | 

18. Gave 10 cents. for a pine-apple, 6 cents for 
- a ball, and 4 cents for a ruler; how many cents were 
given for the whole ? 

19. How many are 9, 7,and6? 4,8, and 6? 9, 
Zyand 5? .T; 4;and 7? 

20. Paid for a coat 10 dollars, for a hat 5 dollars, 
and for a vest 3 dollars ; how much was paid for the 
whole ? 

21. How many are 10 and 5? 10 and 9? 10 and 
7? 10 and 6? 10 and 8? 


16 ADDITION. 


22. If your brother should give you 10 apples, 
your uncle 4 apples, and your father 8 apples, how 
many apples would you then have ? 

23. Three boys, James, Henry, and Charles, went 
a fishing; James caught 10 fishes, Henry 8, and 
Charles 6 ; how many did they all catch? 10, 8, and 
6 are how many ? 

24. Lucy bought some pins for 10 cents, some 
thread for 9 cents, and some tape for 4 cents; how 
much did they all cost? 10, 9, and 4 are how 
many ? 


LESSON VI. 


10. 1. How many are 1 and 10? land 20? 1 
and 30? land40? land50? land60? land 
70? Land 80? land 90? 

2. How many are 1 and 11? 1 and 22? land 
338? land 44? Land55? land 66? 1 and 77? 
land 88? 1 and 99? 

3. How many are 2 and 11? 2and 21? 2 and 
81? 2and 41? 2and51? 2and61? 2and 71? 
2and 81? 2and 91? 

4. How many are 2 and 9? 2 and 19? 2and 
29? 2and.39? 2and 49? 2and 59? 2 and 69? 
2and 79? 2and 89? 2 and 99? 

5. How many are 8 and 8? 8 and 18? 38 and 
28? 38and 388? 8and 48? 3and 58? 8 and 68? 
3and 78? 38and 88? 3 and 98? 

6. How many are 4 and3? 4 and 13? 4 and 
23? 4and83? 4and 43? 4and 53? 4 and 63? 
4and 73? 4and 83? 4 and 93? . 


ADDITION. Te 


7. How many are 5 and 5? 5 and 15? 65 and 
er > and 667) bana 46°? 5 and’oo? 5 and'65? 
5and 75? Sand 85? 5 and 95? 

8. How many are 6 and 4? 6 and 14? 6 and 
94? Gand 34? 6 and 44? Gand 54? 6 and 64? 
6 and 74? 6and 84? 6 and 94? 

9. How many are 7 and 6? 7 and 16? 7 and 
96? Tand 36? YTand46? YT and 56? 7 and 66? 
Tand 76? Tand 86? T7 and 96? 

10. How many are 8and7? 8 and 17? 8 and 
2h? sSiand 31? Sand 47? 8 and 57? 8 and 67 ? 
S8and 77? 8and 87? Sand 97? 

11. How many are 9 and 4? 9 and 14? 9 and 
94? Q9and 34? QYand 44? Yand 54? YO and 64? 
Qand 74? Qand 84? 9 and 94? 

12. How many are 6 and 6? Gand16? Gand 
26? Gand 36? 6and 46? 6 and 56? 6 and 66? 
Gand 76? 6and 86? 6 and 96? 


LESSON VII. 


17. 1. Count by 2’s from 1 to 23. 
SoLuTion. —1, 3, 5, 7, 9, 11, 18, 15, 17, 19, 21, 23. 
2. Count by 3’s from 1 to 81. From 45 to 68. 
8. Count by 4’s from 0 to 86. From 50 to 82. 
4. Count by 5’s from 8 to 43. From II to 46." 
5. Count by 6’s from 7 to 49. From 5 to 53. 
6. Count by 7’s from 2 to 51. From 4 to 46. 
7. Count by 8’s from 4 to 52. From 1 to 41. 
8. Count by 9’s from 5 to 59. From 0 to 63. 
9. How many are 17 and 4 and 3? 
10. How pees are 11 and 9 and 8 and 2? 


18 ADDITION. 


11. How many are 16 and 5 and 7 and 3? 
12. How many are 23 and 6 and 5 and 4? 
13. How many are 20 and 8 and 9 and 7? 
14. How many are 13 and 7 and 9 and 2 ? 
15. How many are 19 and 6 and 5 and 3? 


DEFINITIONS. 
12. What is the sign of addition? The Sign of 
Addition is an erect cross, +, called plus. 


Thus, 3 + 2, is read, three plus two, and denotes that 3 and 2 are 
to be added. 


13. What is the sign of equality? The Sign of 
Equality is two short parallel horizontal lines, =, 
and is read equals or equal to. 

Thus, 3 + 2 = 5, is read three plus two equals 5. 


LESSON VIII. 


14. 1. Charles gave 15 cents for an arithmetic, 
10 cents for a grammar, and 8 cents for a writing- 
cn what was the cost of the whole ? 

. 15 + 10-+ 8 are how many? 

5 Bought 12 bales of cotton, 6 bags of rice, and 2 
boxes of sugar; what is the number of articles pur- 
chased ? 

4, 12 + 6-4 2 are how many? 

d. A lady purchased some silk for 25 dollars, and 
a shawl for 5 dollars; how much did she give for 
both ? 

6. A man bought.a cow for 35 dollars, and a calf 
for 5 dollars ; how much did both cost ? 

7. 85 + 5 are how many ? 

8. If a wagon is worth 50 dollars, a saddle 9 


ADDITION. 19 


dollars, and a whip 1 dollar, what is the value of the 
whole ? 

9. A boy found 62 chestnuts under one tree, and 
20 under another ; how many did ai find in all ? 

10. 62 -+10-+ 10 are how many ? 

11. 84 + 26 + 6 are how many? 

12. A gentleman gave 46 dollars for a watch, T 
dollars for a chain, and 2 dollars for a key; how 
many dollars did he pay for the whole ? 

13. 46 + 7 + 2 are how many? 

14. Lucy had 70 pins in a cushion, and put in 20 
more; how many had she then in the cushion ? 

15. I gave 80 apples to Peter, and had 20 apples 
left ; how many did I have at first ? 

16. 60 + 20 are how many ? 

17. 85 + 20 + 15 are how many ? 

18. New York has 59 counties, Delaware has 3, 
and Rhode Island 5; how many counties have the 
three States ? 

19. A man gave 64 dollars for a piece of land ; it 
cost him 10 dollars to fence it, and 2 dollars to have 
_ it plowed ; what was the whole cost? 

20. A farmer raised 40 bushels of oats, 50 bushels 
of corn, and 20 bushels of turnips ; how many bush- 
els in all did he raise ? 

21. Rufus received 40 cents on his birthday, and 
40 cents at Christmas; how many cents did he re- 
ceive in all? 

22. A farmer kept his sheep in 4 pens; in the first 
there were 20, in the second there were 10, in the 
third there were 8, and in the fourth there were 6; 
how many sheep did he have ? 


20 SUBTRACTION. 


23. My book-case has 4 shelves; the first shelf 
contains 16 books, the second 12 books, the third 7 
books, and the fourth 6 books ; how many books are 
there in the book-case ? 

24. A man started ona journey ; the first day he 
traveled 80 miles, the second day 10 miles, and the 
third day 9 miles; how many miles did he travel ? 

25. Edward bought a vest for 98 cents, some but- 
tons for 12 cents, and some thread for 6 cents; what 
was the whole cost ? 

26. 834 17+ 3 +7 are how many? 

27. 22 + 18 + 25 + 3 are how many ? 


SUBTRACTION. 


LESSON IX. 


15, 1. Henry had 2 apples and gave 1 of them 
to Arthur ; how many had he then left. 

SoLution. — Henry had 2 apples and gave 1 of them to Arthur; 
he then had left 2 apples less 1 apple, or 1 apple. 

2. James had 8 pencils, and gave 1 away; how 
many pencils did James then have ? 

8. Lucy had 4 books, and gave 2 of them to Jane; 
how many books did she then have ? 

4. If I have 5 peaches, and should eat 3 of them, 
how many should I have left ? 

5. Charles had 6 doves, but the cat caught 3 of 
them ; how many did he then have ? 

6. Rufus caught 7 fishes, and threw 4 of them 
back into the water ; how many had he left ? 


SUBTRACTION. piel 


7. Lydia had 8 nuts, but has eaten 4 of them; 
how many has she left ? 

8. I had 9 sheets of paper, but have given 5 of 
them to Charles; how many have [ left ? 

9. William had 8 pears, but has given 6 of them 
to his teacher; how many pears has he left ? 

10. William caught 10 squirrels, but 6 of them 
were allowed to escape ; how many were retained ? 

11. Thomas had 12 cents, but has spent 7 of 
them ; how many has he left ? 

12. Gave 138 dollars for a barrel of flour, and 8 
dollars for a tub of butter; how much more did the 
flour cost than the butter ? 

13. A farmer sold 16 sheep, and 8 lambs; how 
many more sheep did he sell than lambs ? 

14. James had 13 chickens, but 6 were taken by 
the hawks; how many remained ? 

15. George planted 19 trees, but only 9 lived ; 
how many died ? 

16. Gave 15 cents for oranges, and 9 cents for 
lemons ; how much more did the oranges cost than 
the lemons ? 

17. Paid 20 cents for nails, and 10 cents for 
brads; how much did the one cost more than the 
other ? 

18. Bought a clock for 10 dollars, and sold it for 
15 dollars ; what was gained ? 

19. John found 12 eggs, and Samuel 8; how many 
more did John find than Samuel ? 

20. A man engaged to labor 17 days, but left at 
the end of 10 days; how many more days had he 
agreed to labor ? 


yA} SUBTRACTION. 


21. Gave 11 dollars to Emily, and 7 dollars to ~ 
Betsey ; how many more dollars were given to Emily 
than to Betsey ? 

22. Paid 20 cents for a penknife, and 2 cents for 
an inkstand ; how much more did the penknife cost 
than the tnlectanidle ? 

23. Sarah is 17 years old, ‘ind Isabel is 9 years 
old ; what is the difference of their ages ? i 


DEFINITIONS. 

16. What is the difference between two numbers? 
The Difference between two numbers is_ that 
which is left after taking the one from the other. 

17. What is subtraction? Subtraction is the 
process of finding the difference between two given 
numbers. 

18. What is the sign of subtraction? The Sign 
of Subtraction is a short horizontal line, —, called 
Minus. 


Thus, 6 — 4, read six minus four, denotes that 4 is to be subtracted 
from 6. 


LESSON X. 


| 19. 1. How many are 4 less 2? 4 less 3? 65 less 
3? Tless5? Tless4? 8 less 6? 

2. How many are 9 less 5? 10 less 9? 11 less 
8? 13 less9? 12less7? 14 ]less6? 15 less 3? 

3. How many are 16 less 6? 19 less 9? 21 less 
10? 25 1ess10? 29 less 9? 24 less 8? 

4. Howmany are 30—10? 42—10? 24—10? 
30 —52:) 20 — 5? .30— 8?) 40 — 2? 

5. Subtract by 3’s from 63 back to 45. From 31 
back to 1. 


SUBTRACTION. yin 


6. Subtract by 4’s from 82 back to 50. From 36 
back to 0. 

T. Subtract by 5’s from 46 back to 11. From 43 
back to 38. 

8. Subtract by 6’s from 53 back to 5. From 49 
back to 7. 

9. A farmer raised 25 bushels of beans, and 11 
bushels of peas; how many more bushels of beans 
did he raise than of peas ? 

10. Henry had 35 pins, and lost 15 of them ; how 
many had he left ? 

11. Mary went a shopping with 40 cents in her 
purse, and when she returned she had only 10 cents © 
remaining; how many cents had she spent ? 

12. I had 14 oranges, and sold 7 of them; how 
many had I left ? 

13. Thomas had 18 birds, and 9 of them flew away ; 
how many birds remained ? 

14. Henry had 12 quarts of berries, and sold 6 of 
them ; how many had he left ? 

15. Thomas recited 25 perfect lessons, and Wil- 
liam only 8; how many more did Thomas recite than 
William ? 

16. Subtract by 7’s from 46 back to 4. From 51 
back to 2. 

17. Subtract by 8’s from 41 back to 1. From 52 
back to 4. 

18. Subtract by 9’s from 59 back to 5. From 63 
back to 0. 

19. Bought a cow for 27 dollars, and sold her for 
24 dollars ; how much did I lose by the bargain ? 


24 SUBTRACTION. 


20. Sold a lot of wood for 20 dollars, and received 
in payment some cloth worth 7 dollars; how much 
was still due ? 

21. Bought a wagon for 28 dollars, and sold it for 
40 dollars ; how much was gained by the bargain ? 

22. How many are 40 — 28? 85—16? 

23. A man paid 14 dollars to one man, and 4 to 
another; how much more did he pay to one than the 
other ? 

24. From a vessel containing 40 gallons, 15 gallons 
leaked out; how many gallons still remained ? 

25. A boy counted his chickens one night, and 
found he had 19; he counted them the next morning, 
and found he had but 14; how many were missing ? 

26. A horse traveled 40 miles one day, and 27 the 
next day; how many more miles did he travel the 
first than the second day ? 

27. Bought a carriage for 60 dollars, and a harness 
for 35 dollars ; how much more did the carriage cost 
than the harness ? 
| 28. A cistern, which holds 90 gallons, was full in 

the morning, but at night there were but 30 gallons 
left ; how many gallons had leaked out ? 

29. If a man is now 50 years old, what was his age 
24 years ago ? 

30. John is 11 years old, and his father 40; how 
many years younger is John than his father ? 

31. How many are 80 —62? 10 — 24? 

32. How many are 60—13? 50—14? 

33. Find the difference between 22 and each of the 
following numbers: 35, 24, 7, 19, 46, 39, 30, 41. 


REVIEW. 25 


“= See 5 
Sa SS 


SS 


Ne 
SS 


Hs = = a 
= = . vi 
y Ye | BF/ 
oy, fe 
== 


== 


=— 


\— 


LESSON XI. 


#0. 1. A farmer has in 3 enclosures 28 sheep. In 
the first there are 10 sheep, and in the second 6 ; how 
many are there in the third ? 


SoLutTion.— 10 sheep and 6 sheep are 16 sheep; 16 sheep from 
28 sheep leave 12 sheep; there are in the third enclosure 12 sheep. 


2. 18— 6+ 10 = how many? 

3. A man had 16 dollars; he paid 4 to one man, 
and 6 to another; how many dollars were left ? 

4. 16 —4—6 = how many ? 

5. Sold a chest of tea for 25 dollars, which was 7 
dollars more than it cost ; how much did it cost ? 


26 REVIEW. 


6. Paid 12 dollars for a barrel of flour, and 9 dol- 
lars for a hundred-weight of sugar; what was the cost 
of both, and how much more was paid for the flour 
than for the sugar ? 

7. John had 29 apples; he gave 9 to his brother, 
T to his sister, and the rest to his mother ; how many 
did he give to his mother ? 

8. 29— 9— 7 — how many ? 

9. James bought a slate for 15 cents, and some 
pencils for 6 cents; if he had at first 30 cents, how 
much more has he to spend ? . 

10. Isabel is 25 years younger than her mother, 
who is 45 years old; what is Isabel’s age ? 

11. How much less than 40 is 25 + 10? 

12. How much less than 48 is 31 + 9? 

13. How much greater than 45 is 59 — 9? 

14. How much greater than 50 is 63 — 3? 

15. How much greater than 63 is 87 —4? 

16. How much more than 40 + 13 is 60? 

17. How much less than 75 is 85 + 20? 

18. John found that, if he had caught 7 fishes 
more, he should have caught 50 fishes; how many 
did he catch ? 

19. Bought one barrel of pork for 20 dollars, and 
another for 16 dollars, and sold the whole for 40 dol- 
lars ; how much was the gain ? 

20. George spent 19 cents for candy, and 21 cents 
for fruit ; how much more would he have to spend to 
_ make 50 cents ? 

21. Thirty-two, and eight, and five, less ten, are 
how many ? 


REVIEW. pd 


22. Twenty-eight, and three, and nine, less eight, 
are how many ? 

23. Forty-one, and six, and three, and nine, less 
seven, are how many ? 

24, Sixty-four, and four, and six, and one, less five, 
are how many ? 

25. Nineteen, and eleven, and seven, less twenty, 
are how many ? 

26. Fifty-nine, and nine, and seven, and five, less 
thirty, are how many ? 

27. Seventy-seven, and seven, and six, and four 
and eight, less two, are how many ? 

28. Eighty-six, and fourteen, and twenty, less five, 
are how many ? 

29. Ninety-nine, and eleven, and ten, and five, less 
twenty, are how many ? 

380. Two men bought a horse, the one paying 90 
dollars, and the other 30 dollars less ; how many dol- 
lars did both pay ? 

31. Henry, who is 19 years old, is 10 years older 
than James, and 3 years older than Arthur ; required 
the ages of James and Arthur. 

32. A farmer has 75 sheep, his son 20, and their 
neighbor as many as both less 15. How many has 
the neighbor ? 

33. What isa unit? What is a number ? 

34. What is the sum of two or more numbers? 
What is addition ? 

35. What is the difference of two numbers? What 
is subtraction ? 


28 MULTIPLICATION. 


MULTIPLICATION. 


—_~— 
LESSON XII. 
21. 1. At2cents each, what will 2 apples cost ? 


SoLuTion. — If one apple cost 2 cents, 2 apples will cost 2 times 2 
cents, or 4 cents. 

2. At 3 cents each, what will 2 lemons cost ? 

3. At 4 cents each, what will 2 oranges cost? 

4. At 5 cents each, what will 2 oranges cost ? 

d. At 6 cents a pound, what will 2 pounds of rice 
cost ? 

6. Bought 2 writing-books, at 7 cents each; what 
did they cost ? 

T. If 1 pound of sugar costs 8 rents, what will 2 
pounds cost ? 

8. If 1 pound of veal costs 9 cents, what will 2 
pounds cost ? 

9. If there are 10 trees on each side of the street, 
how many are there on both sides ? 

10. What cost 2 quarts of berries, at 11 cents a 
quart ? 

11. What cost 2 pine-apples, at 12 cents each ? 

12. What cost 3 pears, at 4 cents each ? 

13. What cost 3 quarts of milk, at 5 cents a quart ? 

14. What cost 3 yards of braid, at 6 cents a yard? 

15. If a horse will trot 7 miles in one hour, how 
far will he trot in 3 hours ? 

16. If I give 8 cherries for 1 apple, how many 
cherries must I give for 3 apples? 


MULTIPLICATION. 29 


17. Bought 3 yards of cloth, at nine cents a yard ; 
how much did it cost ? 

18. If a ship sails 10 miles in 1 hour, how far 
will it sail in 3 hours ? 

19. If 3 boys have 11 marbles each, how many 
have they in all ? 

20. What cost 3 loaves of bread, at 12 cents a 
loaf ? 

21. What cost 4 bushels of cranberries, at 3 dol- 
lars a bushel ? 

22. At 4 dollars a yard, what will cost 4 yards of 
broadcloth ? 

23. What cost 5 vests, at 4 dollars each ? 

24. At 4 cents a pound, what cost 6 pounds of 
rice ? 

25. What cost 7 cords of wood, at 4 dollars a cord? 

26. What cost 10 skeins of silk, at 4 cents a 
skein ? : 

27. If you can buy 4 nuts for 1 cent, how many 
nuts can you buy for 8 cents? For 9 cents? For 
11 cents? For 12 cents? 

28. How many are 5 times 5? 5 times 6? 5 
times 8? 5 times 9? 

29. At 5 cents each, what cost 7 lead-pencils? 10 
lead-pencils? 11 lead-pencils? 12 lead-pencils ? 

30. When 6 dollars are paid for a cord of wood, 
what must be paid for 5 cords? For 6 cords? For 
7 cords ? 

31. How many are 6 times 8? 6 times 9? 6 
times 10? 6times11? 6 times 12? 

32. If a horse travel 7 miles in 1 hour, how far 


30 MULTIPLICATION. 


will he travel in 7 hours? In 9 hours? In 11 hours? 
In 12 hours ? 

33. At 7 cents a pound, what will 8 pounds of beef 
cost? 10 pounds? 6 pounds? 12 pounds? . 


DEFINITIONS. 

22. What is multiplication? Multiplication 
is the process of taking one of two given numbers as 
many times as there are units in the other. 

23. What is the product of two numbers? The 
Product of two numbers is the result of multiply- 
ing the one by the other. 

24. What is the sign of multiplication? The 
Sign of Multiplication is an inclined cross, X 
read multiplied by. 

Thus, 5 X 4 is read, five multiplied by four. 


LESSON XIII. 


25. 1. Four times three are how many ? 
2. Three times two are how many ? 
3. Seven times three are how many ? 
4, Four times four are how many ? 
5. Five times two are how many ? 
6. Three times seven are how many ? 
7. Five times four are how many ? 
8. ‘T'wo times six are how many ? 
9. Six times five are how many ? 
10. Five times three are how many? 
11. Six times four are how many ? 
12. Five times six are how many ? 
138. Hight times six are how many ? 


MULTIPLICATION. 


. Seven times five are how many ? 

. Six times six are how many ? 

. Seven times four are how many ? 

. Six times three are how many ? 

. Seven times seven are how many ? 
. Eight times five are how many. 

. Eight times four are how many ? 

. Nine times three are how many ? 
.,T'wo times ten are how many ? 

. Three times eight are how many ? 
. Four times nine are how many ? 

. Five times seven are how many ? 

. Six times two are how many ? 

. Seven times eight are how many ? 
. Ten times three are how many ? 

. Ten times six are how many ? 

. Nine times four are how many ? 

. Nine times five are how many ? 

. Seven times naught are how many ? 
. Three times three are how many ? 
. Eleven times two are how many ? 
. Twelve times one are how many ? 
. Ten times seven are how many ? 

. Nine times six are how many ? 

. Twelve times two are how many ? 
. Eleven times four are how many ? 
. Ten times eight are how many ? 

. Twelve times five are how many ? 
. Nine times eight are how many ? 

. Eight times eight are how many ? 
. Seven times six are how many ? 


31 


Bie MULTIPLICATION. 


45. Eleven times three are how many ? 
46. Eleven times five are how many ? 
47. Ten times nine are how many ? 

48. Eleven times six are how many ? . 
49. ‘Twelve times four are how many ? 
50. Eleven times seven are how many ? 
51.. Eleven X eight = how many ? 

52. Twelve X six = how many? 

53. Twelve X seven = how many ? 
54. ‘Twelve X nine = how many ? 

50. Eleven X nine = how many ? 

56. Twelve X eight = how many ? 

57. Eleven X twelve = how many ? 
58. Eleven X eleven = how many ? 
59. Twelve X ten = how many? 

60. Twelve X twelve = how many ? 


LESSON XIV. 


26. 1. If 4 men can do a piece of work in 8 days 
how long will it take 1 man to do it? 

So._urion. — If it takes 4 men 8 days to do a piece of work, it will 
take 1 man, 4 times 8 days, or 32 days. 

2. If 4 men can do a piece of work in 8 days, how 
many men will it take to do it in 1 day? 

3. If 5 men can reap a field in 7 days, how long 
will it take 1 man ? 

4. If 10 men can reap a field in 9 days, how many 
men will it take to reap it in 1 day ? 

5. If a quantity of provisions will supply 11 men 
8 days, how long will it supply 1 man ? er 

6. Multiply from 2 times 2, to 12 times 2. 


MULTIPLICATION. a 


7. Multiply from 0 times 3, to 12 times 3. 
8. Multiply from 0 times 4, to 12 times 4. 

. 9. Multiply from 0 times 5, to 12 times 5. 

10. Multiply from 0 times 6, to 12 times 6. 

11. Multiply from 0 times 7, to 12 times 7. 

12. Multiply from 0 times 8, to 12 times 8. 

13. Multiply from 0 times 9, to 12 times 9. 

14. Multiply from 0 times 10, to 12 times 10. 

15. Multiply from 0 times 11, to 12 times 11. 

16. Multiply from 0 times 12, to 12 times 12. 

17. Multiply 16 by each of the following num- 
bersee by 4. -9,.-2,.8,;-3, 11: 

18. Multiply 19 by 2. By 7. By 10. By 12. 
By 6. By 8. | : 

19. If 6 pipes of equal size can together fill a cis- 
tern in 12 hours, in how many hours could one of 
them fill it? 

20. How many men must be employed to do a 
piece of work in one day, when it takes 11 men 12 
days to do it ? | 
_ 21. If 12 men can dig a ditch in 12 days, how long 
will it take one man ? 

22. How many men must be employed to harvest 
a field in one day, when it takes 10 men 8 days to 
harvest it ? 

23. If a pineapple is worth 7 oranges, how many 
oranges are 9 pineapples worth ? 

24. If a barrel of flour is worth 8 yards of cloth, 
how many yards of cloth are 12 barrels worth ? 

25. At 8 dollars a cord, what will 11 cords of 


wood cost ? 
3 


34 | REVIEW. 


REVIEW. 
—~—— 


LESSON XV. 


27. 1. James bought 3 oranges, at 5 cents each, 
and 6 lemons, at 2 cents each; how much did the 
whole cost ? 

2. Susan bought 8 yards of cotton cloth, at 9 cents: 
a yard, and 4 skeins of thread, at 2 cents a skein; 
what was the cost of the whole ? 

3. A lady bought 8 pounds of sugar, at 11 cents a 
pound, and: paid 8 dozen of eggs, at 10 cents a dozen, 
-and the remainder in money ; how much money did 
she pay ? 

4. How much more will 7 quarts of currants, at 7 
cents a quart, cost, than 8 quarts of berries, at 6 cents 
a quart ? 

5. How much more is 8 times 8 than 7 times 9? 

6. How much more is 8 times 9 than 10 times 7? 
Than 6 times 12 ? s 

7. If two men start from the same place, and 
travel in opposite directions, the one traveling at the 
rate of 8 miles an hour, and the other at the rate of 4 
miles an hour, how far apart will they be at the end 
of 5 hours ? 

8. Bought 6 cords of wood, at 8 dollars a cord, and 
handed in payment 5 ten-dollar bills; how much 
change should be received back ? 

9. Two men start 50 miles apart, and travel to- 
wards each other, the one at the rate of 4 miles an 


REVIEW. 35 


hour, and the other at the rate of 8 miles; how far 
apart will they be at the end of 5 hours ? 

10. How much more is 10 * 10 than 11 x 9? 

11. In a certain orchard there are 10 rows of trees, 
with 11 trees in each row; how many trees are there 
in the orchard ? 

12. A farmer sold 9 sheep, at 5 dollars apiece, and 
5 lambs, at 3 dollars apiece; how much did he get 
for them all ? 

13. A tailor has a piece of broadcloth containing 
33 yards; if he should cut from it 13 yards, what 
will the remainder be worth, at 4 dollars a yard ? 

14. Bought 6 writing-books, at 8 cents apiece, and 
5 more, at 6 cents apiece, and sold the whole for 90 
cents ; how much was made by the sale ? 

15. A farmer has his wheat in 5 bins, containing 
10 bushels each ; how much is the whole worth, at 2 
dollars a bushel ? | 

16. Five times twelve, less ten, plus fifteen, are 
how many ? 

17. Four times fifteen, less twenty, plus six, plus 
twelve, are how many ? 

18. Five times twenty, less twenty-five, are how 
many ? 

19. Eight times eleven, plus twelve, less thirty, 
are how many ? 

20. If a man earns 50 dollars in 5 weeks, and 
pays of his earnings 3 dollars a week for board, how 
much will he have left ? 

21. If one plow is worth 3 cords of wood, how 
many cords will 15 plows cost ? 


36 DIVISION. 


22. If a man earns 100 cents a day, and pays out 
for family expenses 60 cents, how much will he have 
left at the end of 5 days ? 

23. By putting in the savings bank 14 dollars a 
month, how much may be saved in 6 months ? 

24. For how much must I sell 6 cows, which cost 
25 dollars each, to gain 25 dollars ? 

25. A boy earns 12 cents every day, and spends 4 
cents ; how much money will he have at the end of — 
12 days ? 

26. George has 15 marbles, and Lewis has 3 times 
as many, less 10; how many has Lewis ? 

27. Laura gathered 4 quarts of strawberries, and 
Mary gathered 3 times as many, less 2 quarts; how 
many did Mary gather ? 


DIVISION. 


Sees 


LESSON XVI. 


28. 1. At 2 cents each, how many peaches can be 
bought for 4 cents ? 

. SoLuTION. — At 2 cents each as many peaches can be bought for 
4 cents, as 2 cents are contained times in 4 cents, or 2 times; 2 peaches 
can be bought. 

2. At3 cents each, how many lemons can be bought 
for 6 cents ? 

3. How many oranges, at 4 cents apiece, can be 
bought for 8 cents ? | 

4. How many pounds of sugar, at 8 cents a pound, 
can be bought for 24 cents ? 


DIVISION. 37 


5. Lucy paid 20 cents for milk, at 5 cents per 
quart; how many quarts did she buy ? 

6. Harry divided 9 apples among his sisters, giving 
3 to each ; how many sisters had he ? 

7. If I walk 4 miles an hour, how long will it take 
me to walk 36 miles ? 

8. John writes 6 lines a day; in how many days 
will he write 18 lines ? | 

9. If,a scholar explains 2 examples in one min- 
ute, in how many minutes will he explain 12 ex- 
amples ? 
10. At 2 dollars a barrel, how many barrels of 
apples can be bought for 14 dollars ? | 
11. If there are 7 days in one week, how many 
weeks are there in 56 days ? 

12. How many skeins of silk, at 3 cents a skein, 
- can be bought for 21 cents ? 

13. How many yards of broadcloth, at 5 dollars a 
yard, can be bought for 25 dollars ? 

14. If 6 nuts cost 1 cent, how much will 24 cost? 

15. At 9 dollars a barrel, how many barrels of flour 
~ can be bought for 18 dollars ? 

16. At 7 cents a pound, how many pounds of rice 
can be bought for 28 cents ? 

17. If 1 bag contains 3 bushels, how many such 
bags will be required to contain 36 bushels ? 

18. If a horse trot 6 miles an hour, how long will 
it take him to trot 30 miles ? 

19. In how many hours will a ship sail 81 miles, 
at the rate of 9 miles an hour ? 

20. At 6 dimes a bushel how many bushels of corn 
can be bought for 36 dimes ? 


38 DIVISION. 


21. How many boxes of strawberries, at 3 dimes 

apiece, can be bought for 33 dimes ? 

22. How many yards of cloth, at 4 dollars a yard, 
can you buy for 40 dollars ? 

23. At 9 cents a quart, how many quarts of mo- 
lasses can you purchase for 45 cents ? 

24. At 8 cents a paper, how many papers of pins 
may be bought for 32 cents ? 

25. If I give 8 cherries for one apne how many © 
apples shall I receive for 48 cherries ? 

26. If you have 30 cents, how many pencils can 
you buy, at 5 cents apiece ? 

27. If it take 11 yards to make one dress, how 
many dresses can be made from 44 yards ? 

28. When coal is 10 dollars a ton, how many tons 
can be bought for 60 dollars ? 

29, If 9 cherries cost one cent, how much will 72 
cherries cost ? 

30. For 63 dollars how many poe can be ree 
at 9 dollars each ? 

31. At 8 dimes a day, how long will a man be in 
earning 64 dimes ? 

32. How much will 60 yards of cloth cost, at the 
rate of 5 yards for a dollar ? 

33. At 12 dollars a week, how long will it require 
to earn 72 dollars ? 

34. For 40 apples how many melons can be pur- 
chased, at the rate of 8 apples for one melon ? 

85. At 9 dimes each, how many turkeys can be 
purchased for 108 dimes ? 

36. If a train of cars moves at the rate of 12 miles 


DIVISION. 39 


an hour, how many hours will it require to move 96 
miles ? 


LESSON XVII. 


29. 1. Nine is how many times 3 ? 

2. Eleven is how many times 4 ? 

Ans. 11 is 2 times 4, with a remainder of 3. 

3. Twelve is how many times 2? 8? 4? 

4. Thirteen is how many times 2? 4? 5? 

5. Fourteen is how many times 2? 17? 

6. Fifteen is how many times 3? 5? 6? 

7. Sixteen is how many times 2? 4? 8? 

8. Seventeen is how many times 2? 3? 5? 

9. Highteen is how many times 2? 38? 6? 9? 

10. Nineteen is how many times 9? 8? 7? 

11. Twenty is how many times 2? 4? 5? 
Oe Gal he | 

12. Twenty-one is how many times 3? 7? 10? 

13. Twenty-two is how many times 2? 11? 

14. Twenty-three is how many times 2? 10? 
MA D2, 

15.. Twenty-four is how many times4? 6? 8? 

16. Twenty-five is how. many times 5? 6? 
TAs ag 

17. Twenty-six is how many times 2? 6? 13? 

18. Twenty-eight is how many times 2? 4? 
7? 14? 

19. Thirty is how many times 2? 3? 5? 6? 

20. Thirty-one is how many times 8? 6? 9? 

21. Thirty-four is how many times 4? 8? 16? 

22. Thirty-four is how many times 6? 8? 10? 


40 DIVISION. 

23. Thirty-five is how many times 5? 7? 8? 
Oem a 4 

24. Thirty-six is how many times 4? 6? 9? 
IRS eeRe 

25. Thirty-seven is how many times 8? 9? 
15? 16? 

26. Forty is how. many times 4? 8? 10? 
Ou. ou @ 

27. Forty-two is how many times 6? 7? 10? 
14? 21? 

28. Forty-five is how many times 5? 9? 10? © 
Lice LS & 

29. Forty-eight is how many times 6? 8? 
12? 16? 

30. Fifty is how many times 5? 7? 9? 10? 

31. Fifty-one is how many times 3? 5? 17? 

32. Fifty-four is how many times 6? 9? 10? 
1Por ls? 

88. Fifty-six is how many times 6? 7? 8? 
9? 14? 

34, Sixty is how many times 3? 4? 12? 
15? 380? 

35. Sixty-four is how many times 4? 8? 16? 
12? 30? 

36. Sixty-five is how many times 5? 8? 10? 
132. 137? 

387. Sixty-nine is how many times 6? 7? 20? 

38. Seventy is how many times 5? 10? 12? 

39. Seventy-two is how many times 8? 12? 

40. Seventy-four is how many times 10? 12? 

41. Seventy-five is how many times 8? 5? 
15? 25? 


DIVISION. 41 


42. Seventy-seven is how many times 7? 9? 


TO? TL? 


LESSON XVIII. 
20. 1. What is one half of 6 apples ? 


So.LuTion. — One half of 6 apples is one of the two equal numbers 
into which 6 apples can be separated, or 3 apples. 


2. What is one third of 9 oranges? 

3. What is one fourth of 8 cents? Of 12 cents? 

4, What is one fifth of 15 dollars? Of 25 hats? 

5. Harry had 6 chestnuts, which he gave in equal 
numbers to his 2 brothers; how many did each re- 
ceive ? 

6. When 4 cords of wood cost 20 dollars, how 
much does one cord cost? 

7. Thomas distributed 10 flowers equally among 
5 of his playmates; how many did each receive ? 

8. If 12 dollars be distributed equally among 6 
men, how many will each receive ? 

9. James has 12 peaches, which he wishes to give 
_ to 4 of his companions ; how many can he give to 
each, if he divides them equally ? 

10. If a man pays 385 cents for 5 pounds of nails, 
-how much are the nails a pound ? 

11. Mary divided 42 apples equally among 7 com- 
panions ; how many did she give to each ? 

12. In an orchard there are 56 trees, standing in 
8 equal rows; how many trees are there in each 
row ? 

18. When 5 yards of cloth are bought for 20 dol- 
lars, what is the price a yard ? 


42, DIVISION. | 


14. If 5 dollars will buy 40 yards of cotton cloth, 
how many yards will one dollar. buy ? 

15. When 27 cherries cost 9 cents, how many 
cherries can be bought for one cent ? 

16. If 8 oranges are worth as much as 12 apples, 
how many apples is one orange worth ? 

17. If 9 yards of cloth cost 108 cents, how much 
will one yard cost ? 

18. When 50 dollars are paid for 10 cords of wood, 
how much is it a cord ? 

19. What is one seventh of 49 apples ? 

20. What is one sixth of 66 oranges ? 

21. 80 apples are 8 times what number of apples? 

22. 99 are 9 times what number ? 

23. One man can do a certain piece of work in 25 
days; how long will it take 5 men to do it? 

24. How many men will reap a field in 6 days, if 
54 men can reap it in one day ? 

25. If one pipe can fill a cistern in 84 hours, in 
how long a time will 7 such pipes fill it ? 

26. How many tons of hay can be bought for 60 
dollars, at 10 dollars a ton? At 12 dollars a ton? 
At 15 dollars a ton ? 

27. If two boats are 50 miles apart, and the one 
gains on the other 5 miles an hour, in how many 
hours will they be together ? 

28. A school, consisting of 120 pupils, is separated 
into 10 equal classes; how many pupils are there in 
each class ? 

29. 3 heifers were bought for 48 dollars; how 
much were they apiece ? 


DIVISION. 43 


30. If a man earns 8 dollars a week, how long will 
it take him to earn 48 dollars? 64 dollars? 

31. How many cloaks, containing 9 yards, can be 
made from 63 yards of cloth? From 72 yards? - 

32. If 51 dollars be divided among 8 men, how 
many dollars will each receive ? 

33. For 72 cents, how many pounds of beef can be - 
bought, at 8 cents a pound? At 12 cents? 

34. If you should have 51 cents, how many writing- 
books could you buy, at 8 cents each, and how many 
cents would you have left ? 

30. If you had 57 dollars, how many sheep could 
you buy, at 5 dollars each, and how many dollars 
would you have left? 

36. If 182 dollars will buy 12 coats, how much 
will one coat cost ? 

37. If you had 83 dollars, how many tons of coal 
at 9 dollars a ton could you buy, and how many dol- 
lars would you have left ? 


DEFINITIONS. 


21. What is division? Division is the proc- 
ess of finding how many times one of two numbers 
is contained in the other; or, of finding one of the 
equal parts of a number. | 

22, What is the quotient? The Quotient is 
the result obtained by dividing one number by 
another. 

33. What is the sign of division? The Sign of 
division is a short horizontal line with a dot above 
and below, +, and is read divided by. 

Thus, 6 -- 2 is read, six divided by two. 


44 DIVISION. 


LESSON XIX. 


34. 1. How many 2’sin4? In10? In 8? In 
6? ©In 12? .Inl62 In 18)? 7 In 207 eine 

2. How many 3’s in 8? In9? In6? In12? 
In 21?, In 15? In 27? In18? In 86:2? In3o? 
-In 33? In 24? 

3. What is one of the four equal parts of 4? Of 
16? Of 28? Of 20? Of 8? Of 382? Of12? OF 
44? Of 48? 

4. Divide by 5, from 5 in 5 to 5 in 60. 


SOLUTION. — 5 in 5 once; 5 in 10 twice; 5 in 15 three times; and 
so on. 


5. Divide by 6, from 6 in 6 to 6 in 72. By T, from 
7 in 7 to 7 in 84. 

6. Divide by 8, from 8 in 8 to 8 in 96. By 9, from 
yin: 9ito°9.1nsL08. 

7. Divide by 10, from 10 in 10 to 10 in 120. By 
11, from 11 in 11 to 11 in 182. 

8. Divide by 12, from 12 in 12 to 12 in 144. 

9. How much is a seventh part of 49? A tenth 
part of 90? 

10. How many is a fourth of 44? A ninth of 63? 

11. 96 + 12—how many? -(2 +9? 88-- a1? 

12. 63 + 9= what number? 45+5? 108 + 


138. 54 ~ 6 = what number? 56+ 7? 110 + 


14. Eighty is how many times 4? 5? 8? 10? 
20? 40? 

15. Eighty-four is how many times 4? 7? 12? 

16. Eighty-five is how many times 5? 8? 12? 


DIVISION. 45 


17. Eighty-eight is how many times 4? 8? 10? 

18. Ninety is how many times 2? 8? 5? 9? 

19. Ninety-two is how many times9? 10? 15? 

20. Ninety-five is how many times 5? 10? 11? 

21. Ninety-six is how many times 6? 8? 12? 

22. Ninety-nine is how many times 38? 9? 10? 
LY? 

23. How many cords of wood can be bought for 
100 dollars, at 4 dollars a cord ? 

24. When a man, having 75 dollars, can buy 9 
‘pigs, and have 3 dollars left, what is the cost of each 
pig ? 

25. What is sugar a pound, if 9 pounds can be 
bought for 54 cents? For 63 cents? For 90 cents ? 


LESSON XX. 


35. 1. When an apple is cut, or divided, into two 
equal parts, what | 
part of the apple is 
each of the parts ? 
What part of any 
thing is one of the 
equal parts ? 

2. When an ap- 
ple is cut, or divid- | 
ed, into three equal 
parts, what part of 
the apple is each of the parts? What part of any- 
thing is one of the equal parts ? 

3. When 2 apples are separated into two equal 
parts, what part of the whole is one of the equal 


46 DIVISION. 


parts? What number of apples is a half of 2 
apples? <A half of four apples ? 

4. How many apples is a half of 3 apples? Of 5 
apples ? 

5. How many apples is a third of 3 apples? Of 4 
apples? Of T apples? 

6. How many apples is a fifth of 6 apples ? ra 
seventh of 8 apples? A ninth of 10 apples? 

T. How many is a sixth of 31? Of 36? Of 55? 

8. How many is a fourth-of 17? Of 25? Of 49? 

9. How many is an eighth of 33? Of 65? Of 
13 ? 

10. How many is a ninth of 46? Of 64? Of 82? 

11. If a bushel of corn cost 60 cents, what will one 
fourth of a bushel cost ? 

12. If a man can earn 43 dollars in a month, 
how many dollars can he earn in one seventh of a 
month ? 

13. 16 is how many 3’s? 17 is how many 4’s? 

14. 871s how many 9’s? 41 is how many 5’s? 

15. 25 is how many 6’s? 57 is how many 7’s ? 

16. 73 is how many 8’s? 82 is how many 9’s? 

17. 89 is how many 11’s? 97 is how many 12’s? 

18. 4 is how many times 38 and how many thirds 
of 83? 5 is how many times 3 and how many thirds 
Ob 8.7. 

19. 5 is how many times 4 and how many fourths 
of 4? 6 is how many times 4 and how many fourths 
of 4? 

20. 11 is how many times 4 and how many fourths 


of 4? 


DIVISION. 47 


21. 27 is how many times 5 and how many fifths 
of 5? | 

22. 47 is how many times 6 and how many sixths 
of 6? 

23. 69 is how many times 10 and how many tenths 
of 10? 

24.57 is how many times 52.6? 7? 8? 9? 
10? 

25. 63 is how many times 4? 5? 6? 7? 8? 
12? 

26. 71 is how many times 6? 7? 8? 9? 11? 
12? 
27. 82 is how manytimes 7? 8? 9? 10? 11? 


28. 97 is how many times 8? 9? 10? 11? 
Pte? : 

29. Tis how many times 2? 38? 4? 

30. How many times is 2 contained in 13? In 
Dawe init, ln. 1972 sIny 21? 

31. How many times is 8 contained in4? In 8? 
sin 162°In 20? In 25? ‘In 38? 

32. How many times 4 in 5? In 10? In 15? 

33. How many times 5in 8? In9? In1i1? In 
Doering) teen 4? o In 49:7 

34. How many times 6in 7? In 15? In 35? 

35. How many times Tin 17? In 46? In 78? 

36. At $9 a barrel, how many barrels of flour can 
be bought for $64 ? 

37. At 8 cents a pound, how many pounds of rice 
can be bought for 78 cents ? 

38. In how long a time will a ship sail 93 miles, at 
the rate of 10 miles an hour ? 


48 REVIEW. 


39. If 11 peanuts cost 1 cent, how much will 100 
pea-nuts cost ? 

40. If strawberries are 6 cents a pint, how many 
quarts can be bought for 62 cents ? 

41. 11 is2 times what number? 38 times? 4 
times? 5 times? 

42. 23 is 8 times what number? 5 times? 4 
times? 7 times? 6 times? 

43. 25 nuts are 12 times what number of nuts ? 

44. How can you divide 3 apples equally between 
© 2 persons ? 

45. If 9 pounds of meat are worth 95 cents, what 
is 1 pound worth ? 

46. At $7 a yard, what costs 1 sixth of a yard of 
broadcloth ? | 

47. If 1 man can do a piece of work in 20 days, in 
how many days can 3 men do it? 


REVIEW. 


—— 


LESSON XXI. 


&6. 1. How many times 5+ 2in 21? In 35? 

. How my times 6 + 4in 50? In 70? 

44 + 22 are 11 times what number ? 

. What is one eighth of 55 +9? Of 63 + 9? 

. How many times 10 in 115—5? In 107—7? 
. How many times 9 less 4 in 63 — 8? 

. Jason had 52 apples, and found 8; he then di- 
vided the whole equally among 4 schoolmates ; how 
many did he give to each ? 


Io Ot BR Co bS 


REVIEW. 49 


8. A man had 25 cows and bought 15; if he should 
distribute them among 5 pastures, an equal number 
to a pasture, how many would there be in each ? 

9. A farmer had 47 bushels of apples; saving 12 
bushels for his own use, he sold the rest in equal 
quantities to 5 persons; how many bushels did each 
buy of him ? | 

10. How many pears, at 3 cents each, will pay for 
2 melons, at 6 cents each ? 

11. How many lemons, at 4 cents each, will pay 
for 4 oranges, at 2 cents ? 

12. 3 times 8 are how many times 6? 4? 11? 

13. 3 times 10 are how many times 6? 5? 7? 

14. At 2 dollars a bushel, how many bushels of 
wheat must be given for 4 barrels of flour, at 8 dol- 
lars a barrel ? | 

15. How many yards of broadcloth, at 4 dollars a 
yard, should be received in payment for 10 sheep, at 
6 dollars each ? 

16. At 8 cents a pound, how many pounds of 
_ sugar can be bought for 6 dozen of eggs, at 12 cents 
a dozen ? 

17. If you should sell 7 quarts of chestnuts, at 8 
cents a quart, how many slates could you buy, at 14 
cents each ? 

18. If you should sell 8 quarts of milk, at 5 cents a 
quart, how many yards of cotton cloth, at 9 cents a 
yard, could you take in pay ? 

19. Bought 9 quarts of cranberries, at 10 cents a 
quart; to pay for them gave raisins worth 10 cents a 
pound; how many pounds did it take? 

4 


50 REVIEW. 


20. 9 times 8 are how many times 24 + 2? 

21. 9 times 12 are how many times 83 + 3? 

22. 10 times 6 are how many times 20 + 4? 

23. Gave 6 cords of wood in exchange for 3 buf- 
-falo-robes, at 12 dollars each ; how much was the 
wood worth a cord ? 

24. Received 25 yards of broadcloth for 5 tons of 
hay, worth 10 dollars a ton; how much did I pay a 
yard for the cloth? 

25. One book contains 10 pages, with 20 lines on 
a page; but a second book, containing the same num- 
ber of lines, has twice as many pages; how many 
lines to a page has the second book? 

26. An orchard contains 8 rows of trees, and yet 
row contains 9 trees; if I should arrange the same 
number of trees in 6 equal rows, how many trees 
would each row contain ? 

27. How much butter, at 20 cents a pound, must 
be given for 8 yards of calico, at 11 cents a yard ? 

28. James bought 4 dozen of lead-pencils, at 25 
cents a dozen, and paid for them in apples, at 10 
cents a dozen; how many dozen of apples did the 
pencils cost ? 

29. Bought 15 yards of cloth, at 6 dollars a yard, 
and 4 yards more, at 5 dollars a yard, and paid for it 
_with 11 loads of hay ; how much was the hay worth 
a load ? 

30. Received 12 tons of coal for 8 loads of hay 
worth 9 dollars a load; how much did the coal cost 
per ton ? 


REVIEW. _ 51 


LESSON: XXII. 
37. 1. If 4 barrels of apples cost 8 dollars, what 


will 5 barrels cost ? 


SoLuTion. — If 4 barrels cost 8 dollars, 1 barrel will cost one fourth 
of 8 dollars, or 2 dollars, and 5 barrels will cost 5 times 2 dollars, or 
10 dollars. 


fase li 3 pounce of butter cost 36 cents, what cost 5 
pounds ? 

3. When 10 cents are paid for 5 rolls of candy, 
how much must be paid for 6 rolls ? 

4. When 5 dollars will buy 15 yards of cloth, how 
many yards will 9 dollars buy ? 

5. If 4 tons of hay cost 40 dollars, what cost 3 
tons ? 

6. When 7 quarts of fruit bring 35 cents, how 
much do 5 quarts bring ? 

7. If 24 brooms cost 6 dollars, how many brooms 
can be bought for 8 dollars ? 

8. If 8 bushels of wheat cost 16 dollars, how much 
will 7 bushels cost ? 

9. What will 9 quarts of milk cost, if 10 quarts 
cost 50 cents ? 

10. If a horse trot 86 miles in 6 hours, how many 
miles will he trot in 11 hours ? 

11. What will 12 yards of broadcloth cost, if 15 
yards cost 75 dollars ? 

12. If a man can earn 90 dollars in 9 weeks, how 
many dollars can he earn in 6 weeks? 

13. If 3 pounds of cheese cost 30 cents, what will 
6 pounds cost ? 


59 _ REVIEW. 


14. What cost 8 yards of cambric, if 6 yards cost 
60 cents ? 

15. What cost 7 weeks’ board, if 9 weeks’ board 
cost 27 dollars ? 

16. What cost 4 tons of coal, at the rate of 10 tons 
for 70 dollars ? 

17. When 56 cents are paid for 4 dozen of eggs, 
how much must be paid for 10 dozen? 

18. If 28 cents will buy 4 quarts of berries, how 
many quarts will 37 cents buy ? 

19. When 64 dollars are paid for 8 barrels of flour, 
how many barrels can be bought for 72 dollars ? 

20. How many pounds of veal can be bought for 
96 cents, when 9 pounds cost 72 cents ? 

21. When 4 quarts of vinegar can be bought for 
86 cents, how many quarts can be bought for 108 
cents ? 

22. When 7 yards of cotton cloth can be bought 
for 84 cents, how many yards can be bought for 120 
cents ? 

23. If 4 dollars will buy 82 yards of cotton cloth, 
how many dollars will buy 40 yards ? 

24. If 4 cents buy 8 apples, how much will 20 
apples cost ? 

25. If 6 copies of a book cost 18 dollars, how much 
will 12 copies cost ? 

26. If 12 barrels of flour cost 84 dollars, what will 
7 barrels cost? 11 barrels? 6 barrels? 10 barrels? 
9 barrels ? : 

27. When 7 cords of wood can be bought for 56 
dollars, how many cords of wood can be bought for 
72 dollars ? 


REVIEW. 53 


28. If 9 men can dig a ditch in 7 days, how long 
will it take 12 men to dig it? 

29. A man bought 12 hushels of wheat, at 2 dollars 
a bushel, and 4 yards of cloth, at 3 dollars a yard, 
and paid for them in work, at 9 dollars a week ; how 
many weeks did he work? 

30. A can travel at the rate of 5 miles an hour, 
and B, 7 miles; they set out from the same point, 
and in the same direction, but B starts after A has 
traveled 30 miles; how long will it take B to over- 
take A ? 

31. Divide each of the following numbers by 7: 
21, 87, 24, 66, 32, 140, 80, 57, 19, 72, and 86. 

32. What cost one barrel of flour if 9 barrels cost 
each of the following sums: 27 dollars, 86 dollars, 
63 dollars, 108 dollars, 126 dollars, 99 dollars ? 

33. If 20 yards of cloth cost 60 dollars, what cost 
each of the following quantities: 11 yards, 21 yards, 
14 yards, 10 yards, 7 yards, 17 yards, 24 yards ? 

34. If 25 oranges cost 100 cents, what cost each of 
the following numbers: 40 oranges, 60 oranges, 64 
oranges, 84 oranges, 88 oranges ? 

35. If 10 men can do a piece of work in 6 days, 
in what time will 15 men do it? 

36. A and B start together and travel in the same 
direction, A traveling 21 miles a day and B 27 miles; 
when they shall be 72 miles apart, how many days 
will they have traveled ? 

37. What is multiplication? What is the product! ? 

38. What is division? What is the quotient ? 


54 FRACTIONS. 


FRACTIONS. 


——_o——. 


LESSON XXIII. 


38, 1. Into how many halves can an apple be 
divided ? | 

2. What is meant by half of an apple ? 

3. In how many halves of an apple can 2 apples 
be divided ? 

4. How many halves of 1 are there in 2? In8? 
Jn 4? 

oO. How many whole ones in 2 halves? In 4 halves? 
In 6 halves? In 8 halves? 

6. How many halves of one orange are there in 
one orange and a half? In two and a half? In three 
and a half? 


——— se 


FRACTIONS. ty 


7. Into how many thirds can an orange be divided ? 

8. What is meant by a third of anything? By 
two thirds of anything ? 

9. How many thirds of 1 are there in 2? In 3? 
InG ein: 9? Ing lO? 

10. How many thirds of 1 are there in 2 and 1 
third? In 4and 2 thirds? In 11 and 1 third? 

11. Into how many fourths can a cake be divided ? 

12. What is meant by one fourth of a cake? By 
two fourths? By three fourths ? 

13. How many fourths of 1 are there in 2? In 5? 
In 7? 

14. How many fourths are there in 1 and 1 fourth? 
In 2 and 38 fourths ? 

~ 15. What is meant by a fifth of anything? Bya 

sixth of anything? By a seventh of anything? 

16. How many ones in 2 halves? In 3 halves? 
In 16 halves ? | 

17. How many ones in 38 thirds? In 4 thirds? In 
12 thirds? 

18. How many ones in 4 fourths? In 16 fourths? 
In 20 fourths? In 25 fourths ? 

19. How many ones in 5 fifths? In 11 fifths? In 
27 fifths ? 

20. How many ones in 6 sixths? In 18 sixths? 


In 48 sixths ? 
DEFINITIONS. 


29. What isa fraction? A Fraction is a part 
of a unit, consisting of one or more of the equal parts, 
which compose the unit. 

40. What is the denominator of a fraction? The 


56 FRACTIONS. 


Denominator of a fraction is the number which 
shows into how many equal parts the unit is divided. 


Thus, three is the denominator of two thirds. 


47. What is the numerator of a fraction? The 
Numerator of a fraction is the number which 
shows how many of the equal parts of the unit are 
taken. 


Thus, two is the numerator of two thirds. 


4%, What is a common fraction? A Common 
Fraction is a fraction expressed in figures, by writ- 
ing the numerator over the denominator with a line 
between ; as, 

One half, written 
Onethird, “ 
Two thirds “ 


One fourth, written 
Two fourths, “ 
Three fourths, “ 


4.3. What is a mixed number? A Mixed 
Number is a whole number with a fraction; as, 
Ten and four elevenths, written 104-; thirty-two and thiiteen 


5 
twenty-seconds, written 3233; etc. 


LESSON XXIV. 
44, 1. How many feet in 1} feet ? 


SoLution. —In 1 foot there are 2 half-feet. In 13 feet, or 13 half- 
feet, there are as many feet as 2 half-feet are contained times in 13 
half-feet, which is 63 times. There are 6} feet in 13 feet. 

2. How many ones in$? In4? In 22? 

3. How many ones in #2? In 48 
4. How many ones in #2? In $4? 

5. How many ones in §3? In72? In 8? 
6. How many ones in 198 


9 
¢. How many ones in 125? In 84% 


Co[do Ciofd BO 
loo PIbo Ble 


8. 

2. 
10. 
iA 
12. 
13. 
14. 
15. 
16. 
EE 
18. 
i. 
20. 
21. 
22. 
23. 
24. 
25. 
26. 
27. 
28. 
29. 
30. 
31. 


FRACTIONS. AY, 


How many ones in #7? In 192? In 9¢? 
How many ones in 4p. ? In 8? In 34? 
How a ones in Lol Po nS? In (10857 
Change 42 to an equivalent Crate ciate 
Change $¢ to an equivalent whole number, 
Change 144 to an equivalent whole number. 
Change 4; ep to an equivalent whole number. 
Change 90 to an equivalent whole number. 
Change & to an equivalent mixed number. 
Change 1 to an equivalent mixed number. 
Change 2° to an equivalent mixed number. 
Change }; 193 to an equivalent mixed number, 
Change §% to an equivalent mixed number. 
Change +43 to an equiyalent mixed number. 
Change }; a, - to an equivalent mixed number. 
Change 4, 130 to an. equivalent mixed number. 
Change 72 to an equivalent fraction. 

Change 9% to an equivalent fraction. 

Change 12+ to a fraction expressing sevenths. 
Change 11% toa fraction expressing elevenths. 
Change 10% to a fraction expressing ninths. 
Change 183 to a fraction expressing thirds. 
Change 1075 to a fraction expressing tenths. 
How do you change a fraction to an equivalent 


whole or mixed number ? 


D2. 


How do you change a mixed number to an 


equivalent fraction ? 


DEFINITIONS. 


45. What is a proper fraction? A Proper 
Fraction is one whose numerator is less than the 
denominator ; as 4, %. 


58 FRACTIONS. 


46. What is an improper fraction? An Im- 
proper Fraction is one whose numerator is not 
less than the denominator; as 4, 2. 

47. What are the terms of a fraction? ‘The 
Terms of a fraction are the numerator and denom- 
inator. 

48. When is a fraction expressed in its lowest or 
smallest terms ? A fraction isin its Lowest Terms 
when no number greater than 1 will divide both its 
_ terms without a remainder. 


LESSON XXV. 


49, 1. In lapple there are how many halves of 
ECC \ anapple? How many 
_~ fourths of an apple? 
_ How many halves of 
an apple are two 
_ fourths of an apple ? 
2. In 1 pie there 
are how many thirds 
\ uENt __. ofa pie? How many 
(OMAK sixths of 3 pie ? 
3. How many thirds of a pie in ¢ of a pie. 


Sotution. — In 1 third of a pie there are 2 sixths of a pie, and in 
4 sixths there are as many thirds as 2 sixths are contained times in 
4 sixths, or 2 times. There are 2 of a pie in 4 of a pie. 
4, Change 58, to sixths. To fourths. To halves. 
5. Which has the smaller terms ,% or 2? 2 or}? 
6. Change ,°; to fifths. 8, to fifths. .8, to halves. 
7. Change 74 to sixths. 4, to its smallest terms. 
8. Change 42 and 34 each to sixths. Each to its 
lowest terms. 


FRACTIONS. 59 


9. Change 12 and 4 to their lowest terms. 
10. Change 3 and }% to their lowest terms. 


11. Change +; and ;8; to their lowest terms. 
12. Change »°; and ?4 to their lowest terms. 


13. Change %8 and 23 to their lowest terms. 
14. Change &? to their lowest terms. 
15. Change $$ and 25, to their lowest terms. 
16. In 3 2 of a pie are how many sixths ? 


eee sntt — In 1 third of a pie there are 2 sixths, and in 2 thirds 
there are 2 times 2 sixths, or 4 sixths. There are in 2 of a pie 4 
sixths. 


Pie In 


coir colo Crbo v9 
Se > Slr oy 
x 2 4 
=) 
ou 
wo 
nS 


there are how many tenths ? 

18. In 4 there are how many fourteenths ? 

ie there are how many twelfths ? 

20. Change 4, 4, and 4 to twelfths. 

21. Change ? and 3 his elghths. 

22. Change 3, #, A 4 to thirtieths. 

23. Change }, 3%, and } to sixths. 

24. Change } to sevenths. 

25. Change $ and 2 to fractions having the same 
denominator. 

26. Change ; 
denominator. 

27. Change }, 4, and } to fractions having the same 
denominator. 


Ro <n is 


— 
=) 


blo “ 
» + 
S 
jon 
coo aH 


An 
ss) 
5 
(os) 

i) 


g to fractions having the same 


DEFINITIONS. 

50. What is reduction of fractions? Reduction 
of fractions is the process of changing their form with- 
out changing their value. 

51. When have fractions a common denominator ? 
Fractions have a Common Denominator when 
they have the same number for a denominator. 


60 FRACTIONS. 


LESSON XXVI. 


&2. 1. Reduce 4 and % to equivalent fractions 
having a common ASuan ators 

2. Reduce 4 and 2 to equivalent fractions having a 
common aenenaeee 

3. Change 3 and +3, to fourths. 

4. Change 3 and @ ; to twelfths. 

5. Change }, 4, ee &, to sixtieths. 

6. Gave 2 of an apple to one boy, ? to another, and 
3 to another. How many fourths were given away ? 
How many whole apples ? 

$+ 2+ 6 are how many fourths? Are how 
many times 1? 

8. Lydia has ? of a dollar, and Mary ? of a dollar ; 
how many dollars have they both ? 

9. Sold 2 of an acre of land to one man, @ to an- 
ee and % to another; how many acres were sold ? 

4+2-+%-+ é are how many times 1? 

a acnond had 7? dollars, and his father gave 
him 3 of a dollar more; how many dollars had he 
then ? 

12. Bought a barrel of flour for 9% dollars, and a 
yard of velvet for 43 dollars ; how much did the whole 
cost ? 

13. James gathered 8} quarts of berries, Frank 4% 
quarts, and Arthur 63 quarts; how many did they 
all gather ? 

14. A man bought 4 of an acre of land at one time, 
and 3 of an acre at another time; how many thirds 


of an acre did he buy ? 


FRACTIONS. 61 


15. Gave 34 of a bushel of corn to one man, and } 
to another ; how many sixths did I give them both ? 

16. Gave } of a dollar to Lydia, and ? to Sarah ; 
to which was the most given ? 

17. A man divided a quantity of fruit among 3 of 
his friends ; he gave } to one, } to another, and % to 
another ; how many fourths did each receive ? 

18. + 4 + 3 are how many fourths ? 

19. A gentleman kept 8 fires in his house, during 
the winter; the first fire consumed 2 of a ton of coal, 
the second 4, and the third 3 of a ton; how many 
sixths did each consume ? How many tons did they 
all consume ? 

20. 3-+ 4 + 4 are how many sixths? How many 
times 1 ? 

21. 58, + To + 1235 are how many times 1? 

22. 34 + 43 + ¢ are how many times 1 ? 

23. 8g + 42+ 4 are how many times 1? 

24. What is the sum of 3 and #? 

25. What is the sum of 2 and 3? 

26. What is the sum of # and 3? 

27. What is the sum of 7 and 7? 

28. $+ # are how many times 1? 

29. 3, + 4 are how many times 1? 

30. 1§ + 23 are how many times 1 ? 

31. 114 + 10} are how many times 1? 

32. What is the sum of }+4-++ 2? 

33. What is the sum of # + 38%, + 2? 

34. What is the sum of 3¢ + 4+ 4? 

535. What is the sum of 11+ 3+ 4%? 

36. A farmer sold 3 of a bushel of peaches to one 


62, FRACTIONS. 


man, # to another, and 2 to another; how many 
bushels did he sell in all? 


LESSON XXVII. 


53. 1. A man who owned { of a ship, sold 3 of 
it ; what part of the ship did he then own ? 

2. If you should give $ of a melon to your brother, 
and retain the rest for yourself, what part would you 
retain ? 

3. If x of an acre are sold from a piece of land 
containing 213 acres, how much land remains ? 

4, Games had 172 dollars, but has spent 22 dollars 
of it; how much has he left ? 

©). From 2575 acres of land there have been sold 
45, acres; how much is left ? 

6. A gentleman owned a ship, but has sold + of 
it; what part does he still own ? 

7. Sarah bought 3 yards of cloth, and gave Ellen 
of a yard ; how much had she left ? 

8. Bought a Bible for 5 dollars, less 3 of a dollar ; 
how much was paid for it? 

9. From a hogshead of wine there leaked out 63 
See: ; how th gallons remained ? 

10. 3 from % leave how many ? 

11. } from 3 leave how many ? 

12. 2 from 12 leave how many ? 

13. 4 eae Wy leave how many ? 

14. 104 less 13 are how many ? 

15. 12 less § are how many ? 

16. 113 — 10} leave how many ? 

17. 16 — 1% leave how many ? 


FRACTIONS. 63 


18. 4 + 3 are how much less than a whole one ? 
19. } + } are how much less than a whole one ? 
20. + + 2 -+ 2? are how much less than 2 ? 

21. 75 — 12% are how many times 1 ? 

22. 181} — 108 are how many times 1 ? 

23. 824 — 48 are how many times 1 ? 


24. George put into the bank at one time 11 dol- 
lars, and at another time 6, dollars; how much 
more must he put in to make up 20 dollars ? 

25. Bought a coat for 11% dollars, and a vest for 
32 dollars and gave in payment two ten-dollar bills ; 
how much change should be received back ? 

26. George is 11,3 years old, Simeon 8,5, and 
Edward 6% ; how much does the sum of their ages 
exceed 5 times 5? 


LESSON XXVIII. 


54. 1. If a family consume 2 of a barrel of flour 
in a week, how much will it consume in 6 weeks ? 

Sorurion. — If in 1 week a family consume 2 of a barrel of flour, 
in 6 weeks it will consume 6 times? of a barrel, which are 12 of a 
barrel, or 22 barrels. Jt will consume in 6 weeks 22 barrels. 

2. What cost 7 yards of cloth at $ of a dollar a 
yard ? 

3. At 3 of a cent apiece, what cost 12 eggs? 

4. At 3 of a dollar a day, how much can be earned 
in 12 days? 

5. At 4 of a dollar, a peck, what cost 5 pecks of 
apples? T pecks? 8 pecks ? 

6. At x4 of a dollar a bushel, what cost 3 bushels 
of potatoes? 8 bushels? 12 bushels? 


64 FRACTIONS. 


7. How many are 4 times 3? 5 times $? 
8. How many are 6 times 3? 7 times #? 
9. How many are 9 times}? 10 times $? 
(10. Ifa peck of corn costs 33; of a dollar, how much 
will 8 pecks cost ? 
11. If a man can reap § of an acre in a day, how 
many acres can 4 men reap in the same time ? 
12. If a man can walk 3} miles in an hour, how 
far can he walk in 10 hours ? 
13. What will 7 chairs cost at 54 dollars each ? 
14. At 6} cents a pound, what cost 9 pounds of 
rice? 10 pounds? 12 pounds? 
15. When eggs are 163 cents a dozen, what cost 3 
dozen? 6 dozen? 
16. What cost 20 bushels of wheat, at 2} dollars a 
bushel? At 23 dollars? 
17. What will 12 yards of silk cost at 23 dollars a 
yard ? 
18. At 61 cents a nail, what cost 4 yards of cloth? 
8 yards? 10 yards? 
19. How many are 4 times 24? 6 times 82? 
20. How many are 6 times 57? 9 times 53? 
21. How many are 8 times 44? 10 times 53? 
22. How many are 7 times 83? 12 times 11,4? 
23. If a horse can trot 93 miles in 1 hour, how far, 
at that rate, can he trot in 9 hours ? 
24. How much can be earned in a year, at 112 
dollars a month? At 10% dollars a month ? 
25. What cost 5 bushels of corn, at 7% of a dollar a 
bushel ? 
26. If a man can reap 1} of an acre in a day, how 
many acres can 12 men reap in the same time ? 


FRACTIONS. 65 


27. What cost 6 pounds of opium, at 42 dollars a 
pound? At 4,% dollars a pound ? 

28. How many are 8 times 53,? 8 times 123? 

29. How many are 9 times 108? 9 times 2,,,? 

30. How many are 10 times 103,? 10 times 
15,9? 10 times 12.7, ? 

Ol. low many are $x 37° 2k « 67) 31 «147 
14x 8? 43 x 9? 


LESSON XXIX. 


55. 1. If a box of oranges is worth 4 dollars, 
what is } of a box worth ? . | 

So.uTion. — If 1 box of oranges is worth 4 dollars, 4 of a box is 
worth } of 4 dollars, which is 4 of a dollar, or 14 dollars. 4 of a box 
is worth 14 dollars. 

2. If a pound of dried apples costs 8 cents, what 
will 3 of a pound cost ? 

3. If a barrel of beef is worth 4 dollars, what 
is ¢ of a barrel worth ? 

4. Whatis,of 4? Of5? Of 7? Of 12? OF 
foe O21? Of.28 ? 

5. Whatis~, of 3? Of5?: Of 6? Of 7? OF 
th? OL to?” Of 20? 

Gayvuacissttot. 4? OL 7? ORD OF 1025 OF 
toc Of by 7° Of 16:7 

7. If 4 oranges are divided equally among 5 boys, 
what part of an orange will each boy receive? How 
much will 2 boys receive ? 

8. If 8 bushels of apples cost 5 dollars, what part 


of a dollar does 1 bushel cost? 8 bushels ? 
5 


66 FRACTIONS. 


9. If 12 chairs cost 9 dollars, what cost 1 chair ? 
What cost 5 chairs? What cost 8 chairs ? 

10. If 8 bushels of corn cost 6 dollars, what cost 3 
bushels ? What cost 5 bushels ? 

11. What cost ? of a pound of butter, at 17 cents a 
pound ? 

12. If 1 pound of cheese cost 12 cents, what will 

3 of a pound cost ? 

13. At 19 cents a yard, what cost 2 of a yard of 
calico? What cost § of a yard ? 

14. If 1 pound of sugar cost 12 cents, how much 
will 32 pounds cost ? 

15. If a man walks at the rate of 8 miles an hour, 
how far will he walk in 22 hours ? 

16. Whatis2of 7? Of 8? Of9?> Or 10geeGT 
Ti?S OF Ta Ora a? 

17. What is 3 0f 22, Of 7? -Of 9? Oris aug 
Tae OUST, SOT oe 

18. How many are #of 5? Of 6? Of10? Of 
Lob OO heme ald oy Oe 4 | 

19. How many are $ of 2? Of 3? Of 6? OF 
10? -Of13?° Of 20? 

20. How many are 3 of 2? Of 4? Of 7? Of 
ite CITA SAT | 

21. How many are 1? times 83? Times 5? Times 
7? Times 9? Times 20? 

22. How many are 2? times 2? Times 8? Times 
9? Times 10? Times 15? 

23. How many are 4 x 84? 6X 31? TX 3? 
etal ets 05K OB 


FRACTIONS. 67 


LESSON XXX. 


56. 1. If one rod of land is worth +2 of a dollar, 
how much is } of a rod worth ? 

Sotution.— If 1 rod of land is worth +2 of a dollar, 4 of a rod is 
worth + of 42 of a dollar, or {8 of adollar. 4 of a rod is worth zx of 
a dollar. 

2. John had } of a dollar, and gave } of it to James. 
What part of a dollar did James receive ? 

ES —+of a dollar is equal to {2, of a dollar. dof %, of a 
dollar is j, of a dollar. James received 1, of a dollar. 

Cr: L of 1 is j,; James received +, of a dollar. 

3. ih gentleman owned 3 of a ship; if he should 
sell 1 of his share, what part of the ship would he 
sell ? 7 


4. How much of a melon is } of 3 of it ? 

5. How much is} of 1? of}? 

6. What is4 of}? of}? fof4? Lofi? 
7. Whatis}of3? tof41? tof1? lof}? 

8. Bee ded! Loft? oft? ofl? 
9. What is ~, of #? ene 2 of $2) essoivse? 
10. What i] Of 2, 2 FOF HEM a of Ge? ot 


tr?) ty Ol $? 

11. A gentleman, owning ? of a farm, sold } of his 
part; what part of the whole farm did he sell ? 

12. If 6 pounds of cheese cost 7 of a dollar, what 
does 1 pound cost ? 

13. If 5 barrels of flour cost 848 dollars, what will 
1 barrel cost ? 

Sorution. — 4 of 348 dollars is equal to 4 of 30 dollars plus $ of 


43 dollars. L of : 30 deviant is 6 dollars and b of 43 or 2§ 9 dollars is 20 


68 FRACTIONS. 


ofadollar. 6 dollars plus 2% dollars are 62% dollars. 1 barrel will 
cost 629 dollars. 

14. If 4 pounds of sugar cost 334 cents, what cost 
1 pound? What is $ of 333? 

15. Sold 9 barrels of apples for 183 dollars ; what 
cost 1 barrel? What is 4 of 183? 

16. What is 4 of 44? of 83? Jjof 51? 1Lof 
103? 

17. What is + of 113? 30f 74? +, of 163? 3 
of 113? 

18. What part of an acre is 4 of +, of an acre? 

SovuTion. — 4 of 5% of an acre is siz of an acre, and 4 of 54 are 4 
times ,7,, or 28 of an acre. 

19. What part of a ship is 3 of 2 of it? 

20. If you should have $ of a barrel of apples, and 
sell 8 of them, what part of a barrel would you sell ? 
21. Whatis}of 2? 2o0f8? 2o0f1? 2of g? 

22. What is 4 of 3? Zo0f 13? fof %? 2of 3? 
yy of 2? 
' 93. What is x, of }? S§ of 3? 3 0f 29? 4 of 49? 
3 of 23? 

24. What cost & of a bushel of corn, at 7 of a dol- 
lar a bushel ? 

25. What is 3 times 53? yy, &X 3? ye xX 4? 
re N A cea KOT 


LESSON XXXI. 


57, 1. Susan divided # of a cake among her 4 
brothers, what part of the cake did each receive. #4 
divided by 4 is what part of 1 ? 

2. Henry divided { of a quart of chestnuts among 
3 boys; what part of a quart did he give each ? 


FRACTIONS. 69 


So.ution. — If 7 of a quart be divided among 3 boys, each boy will 
receive } of 7, or gz of a quart. 

3. How much is # divided by 4? $ divided by 3? 

4. If 6 yards of calico cost 3 of a dollar, what will 
1 yard cost ? 

5. If 4 men can mow § of a field in a day, what 
part of the field can one man mow ? 

6. How much is ? divided by 6? 8 divided by 4? 

T. If 5 pounds of sugar cost 33 of a dollar, what 
part of a dollar will 1 pound cost ? 7 

8. When 6 pounds of sugar cost 3 of a dollar, 
what part of a dollar will 1 pound cost ? 

9. How much is 3} divided by 2? 3 divided by 6? 

10. Divide 24 by 8? $83 by T? 3 by 5? 

11. Divide 22 by 9? 48 by 10? 42 by 6? 

12. When 12 loaves of bread can be bought for 
Yes Of a dollar, what part of a dollar will buy 1 loaf? 

13. A man bought 8 pounds of butter for 2,4, dol- 
lars ; how much was it a pound ? 

14. If 5 barrels of flour cost 314 dollars, what is 
the cost of one barrel ? 

15. When 4 bushels of corn cost 32 dollars, how 
much does 1 bushel cost ? 

16. What is 234; divided by 8? 81} divided by 5? 
33 divided by 4? : 

17. Jones paid 82 dollars for 6 books, what is that 
a book ? 

18. Bought 10 yards of cloth for 62 dollars, how 
much is that a yard? 

19. What is 83 +6? 623+10? 92, +12? 

20. Whatis10} +138? 113 +11? 16} + 3? 


70 FRACTIONS. 


21. What is 152 +9? 128+ 8? 7—11? 

22. A man bought 9 bushels of apples for 7} dol- 
lars; what was that a bushel ? 

23. A boy received 84 dollars for 6 days’ work ; 
what was that a day ? 

24. If 31} dollars are divided among 10 men, how 
much will be each man’s share ? 

25. What is 71 divided by 9? 8% divided by 6? 
311 divided by 10 ? 

26. If a man can do a piece of work in 11} days, 
in what time can 12 men do it? 


LESSON XXXII. 


58. 1. How many yards of cloth, at } of a dol- 
lar a yard, can be bought for 2 dollars ? 

2. At ? of a dollar a day, how long will it take a 
man to earn 9 dollars ? 

SoLtuTion. —9 dollars are equal to 36 fourths, and 3 fourths are 
contained in 36 fourths, 12 times. It will take 12 days to earn 9 
dollars. 

3. Susan distributed 4 pears among some school- 
mates, giving to each 2 of a pear; how many school- 
mates were there ? 

4, If you should spend 3 of a dollar a day, how 
long will you be in spending 12 dollars ? 

5. How many times2in 9? ?in4? 2in12? 

6. At 4 of a dollar a bushel, how many bushels of 
oats can be bought for 10 dollars ? 

Tt. At 7 of a dollar a yard, how many yards of 
cloth can be bought for 5 dollars ? 

8. Henry can saw 3 of a cord of wood in a day ; in 
how many days can he saw 4 cords? 


FRACTIONS. 71 


9. How many times is £ contained in 10? 4 in 5? 

10. How many times is 8 contained in4? #4 in 5? 

11. How many times is ? contained in 4? In 6? 

12. How many pens at 1y cents can be bought for 
12 cents ? 

18. How many times 1}in 12?. 2}in 9? 313in 
13 ? 

14. At 24 dollars a bushel, how many bushels of 
wheat can be bought for 10 dollars? 

15. How mich cloth at 23 dollars a yard can be 
bought for 6 dollars ? 

16. How many times is 5} contained in 17 ? 

17. How many is4 +2? 6+14? 10+ 21? 

18. How many is 11+? 10+ 53? 0 + 49? 


LESSON XXXII. 


59. 1. Ati of a dollar each, how many. tickets 
can be Orns for 4 of a dollar ? 

2. If a horse trot } of a mile in a minute, how 
long will it take him £ trot # of a mile? 

3. At 7, of a dollar a pound, how many pounds of 
starch can ive purchased for 2 of a dollar ? 

4. How many times is } naniathed Ind? 434 ine? 
ps In 2? | 

5. At @ of a dollar a day, in what part of a day 
will a man earn 3 of a dollar ? 

So.ution.—1 ofa ete is 3 of a dollar. At 8 of a dollar a day 
a man will earn 1 in } of a day, and 3 in 3 times 1 or 3 ofa day. 

6. At @ of a dollar a day, in what part of a day 
will a man earn 2 of a dollar ? 

7. Ifa man can do a piece of work in % of a day, 
what part of the work can he do in 3 of a day? 


pe FRACTIONS. 


8. How many times is 3 contained in §? 

9. How many times is ? contained in 4,7? 

10. If a horse eats 4 if a ton of ee in 1 week, 
how many weeks will he be in eating 8 of a ton? 

11. How many times is $ contained in 4% ? 

12. How many pounds of tea, at 3 of a dollar a 
pound, can be bought for 3 of a dollar? 

13. How many times is # contained in 2}? 

14. How many times is ? contained in ,, ? 

15. How many times is 3} contained in 675 ? 

16. How many times is 4 contained in 11}? 

17. How many times is 3 contained in 3 ? 

18. How many times is } eontatned@ in 34? 

19. How many times is 6} contained in 128 ? | 

20. If 1 man can do a piece of work in 5k days, 
how many men can do it in 2} days ? 

21. How many men will be required to reap 24 
acres, while 1 man is PIS 1% acres ? 

22. When $1 will buy 23 gallons of molasses, how 
many dollars must be paid ihe 54. gallons ? 

23. At @ of a dollar a day, in how many days all 
a man earn $6}? 

24. How many is 184 +2? 223 +48? 58 — 8? 

25. How many is 64 —1}? 63—14? 62 —81? 

26. If 1 yard of cloth costs 13 dollars, how many 
yards can be bought for 53 dollars ? 

27. At % of a dollar each, how many baskets can 
be bought for 3} dollars ? | 

28. How many pounds of coffee at 2 of a dollar a 
pound can be bought for 43 dollars ? 

29. How many yards of cloth at 2 of a dollar a yard — 
can be bought for 6% dollars ? 


REVIEW. 73 


REVIEW. 


SS 


LESSON XXXIV. 


60. 1. If a melon cost 38 cents, what will } of a 
melon cost ? 

2. At 9 dollars a yard, what will # of a yard cost ? 

3. At 16 dollars a ton, what will 7 of a ton cost ? 

4. At 12 dollars a barrel, what will 112 barrels 
of flour cost ? 

5. When a man is working for 15 dollars a week, 
how much does he earn in 8} weeks ? 

6. At 16 cents a pound, what cost 5? pounds of 
sugar ? 

7. At 8 dollars a cord, what cost 43 cords of wood ? 

8. At 6 dimes a bushel, what cost 102 bushels of 
corn ? 

9. A teacher being asked how many scholars he 
had, replied that the smallest number that ever had 
been present was 18, which was just $ of his whole 
number ; how many had he ? 

10. Sold a horse for $150, which was 3 of what he 
cost; what did he cost ? 

11. I have 4 dollars, which is } of what I divided . 
among 10 men; how much did each receive ? 

12. William has 63 cents in his pocket, which is 
2 of what he has in his money-box ; how much has 
he in his money-box ? 

13. A boy, being asked how many chickens he 
had, answered that his largest brood contained 20, 


74. REVIEW. 


which was # of the whole number, and the whole 
number was 5 times as many as he had in the smallest 
brood ; how many had he, and how many were there © 
in the smallest brood ? 

14. A farmer had 42 sheep, and sold 4 of them to 
5 of his neighbors, each receiving an equal number ; 
how many did each receive ? 

15. I had 24 cherries, but have divided $ of them 
equally among 10 children; how many does each re- 
ceive ? 

16. A gentlemen had 36 pears, and gave 4 of them 
to Frank, and divided the remainder equally among | 
his 5 brothers; how many did Frank receive more 
than each of his brothers ? 

‘17. At 10 cents a pound, what cost 20 pounds and 

3, of a pound of raisins ? 

‘38. At 18 cents a pound, what cost 8 pounds and § 
of a pound of butter? 

19. Jobn has 20 cents, which is # of 5 times as 
many as Joseph has; how many has Joseph ? 

20. Emma is 12 years old, and % of her age is just 

Z of her sister’s age; what is her cae sage? 

21. A pier of a certain bridge stands 10 feet in the 
water, which is ? of the height of the pier lacking 5 
feet ; what is the height of the pier? 

22. Bought 4 pounds and 3 of a pound of rice at 
8 cents a pound, and paid for it with berries at 5 
cents a quart; how many quarts did it take ? 

23. Bought a watch for 40 dollars and a chain for 
5 dollars more than 2? the cost of the watch ; what 
did both cost ? 


REVIEW. 75 


24. 4 of Edward’s money is 5 times Henry’s, 
and Henry has 11 dollars; how much has Edward ? 

25. 2 of 24 is x of the number of books which 
James owns ; how many does he own ? 

26. 4 of 28 is $ of what number? 

27. 4 of 16 is } of what number ? 

28. & of 42 is 2 of what number ? 

29. 2 of 48 is § of what number ? 

30. 34 of 22 is 38 of what number ? 

31. % of 32 is $ of what number ? 

32. $ of 56 is 12 times what number ? 

33. # of 75 is 22 times what number ? 

84. Bought a cow and a horse; the cost of the cow 
was 82 dollars, and that of the horse was 2 times 8 
of the cost of the cow; what was the cost of the 
horse ? 


nN 


be tee | 


LESSON XXXV. 

61. 1. A market woman sold some butter, eggs, 
and milk; for the eggs and milk she received $4, 
which was 3 of what she received for the butter ; how 
much did she receive for the butter ? 

2. Sold 2 of an acre of land for $24; at how much 
an acre was it sold ? 

3. If James can run 60 rods in a minute, and 
John 2 as far, how long will it take John to run 15} 
rods ? 

4, 28 is of a number; what is that number ? 

5. 36 is 7% of a number; what is that number ? 

6. If 4 of a firkin of butter cost $8, what will 2 of 
a firkin cost ? 

1. 4 of 1 of 24 is 3 of what number ? 


76 REVIEW. 


8. 4 of 2 of 15 is 2 of what number ? 

9. If a bushel of potatoes is ? of a barrel, and cost 
$114, how much will 1 barrel cost ? 

10. A and B own some wood ee A’s share 
is $; it is sold, and A receives as } of his part of the 
reese $24; how much did the soe sell for? How 
much was B’s part of the proceeds ? 

11. A teacher, being asked how many scholars he 
had, answered that 20 of them were girls, and ? of 
them and 4 more were boys; how many boys were 
there? How many scholars in all ? 


So.ution. — As the number of scholars is 4 of itself, 20 scholars 
-|. 4 scholars must be the remaining 8. If 3 of the number is 24, + 
of the number is 4 of 24, or 8, and 8, or the whole number of scholars, 
is 5 times 8, or 40. The number of boys must be the difference be- 
tween 40 and 20, which is 20. 


12. 14 is ? of 7 of what number? 

13. 18 is 2 of ; of what number ? 

14. John Teake sold a horse for 60 dollars, which 
was 2 times ? of what he gave for it; how much did 
he gain by the sale ? 

15. Bought a piece of land for 64 dollars, and ein 
4 of 4 of it for 28 dollars ; how much will be gained 
if Ke rest be sold at the same rate ? 

16. # of. a pole is above ground, and 3 feet is } of 
the part in the ground; what is the length of the 
pole ? 

17. George spent 6 elevenths of his money for a 
suit of clothes; he then paid 2 dollars for a hat, 
which was just 1 fifth of all he had left; how many 
dollars had he at first ? 

18. 35 is & of § of what number ? 


REVIEW. CE 


19. A pole stands 3 fifths in the water, 1 half of 
the remainder in the mud, and 4 feet above the water ; 
what is the length of the pole? 

20. If 3 of a dozen of eggs cost } of a dollar, how 
many dozen can be bought for 1 dollar ? 

- 21. 86 is 3? of how many times 8? 

22. 52 is $¢ of how many times 13? 

23. John Doe and Richard Roe enter into a specu- 
lation together, with a certain capital, 7 of which 
was contributed by John, and the remainder by Rich- 
ard; on dividing their gains, John received 60 dollars 
as his share; how much was Richard’s share ? 

24. If 10 is ¢ of some number, what is 2 of the 
same number ? 

25. If 12 is % of some number, what is 2 of the 
same number ? 

26. What number added to 2 times 2 of 87 will 
make the number 18 ? 

27. What number added to 5 times 2 of 80 will 
make the number 65? 

28. What number taken from 4 times 2 of 19 will 
leave 504 ? 

29. What number taken from 3 times 8 of 22 will 
leave 100? 

30. 40 is £ of how many times 16 ? 

31. What number added to 8 times 2 of 24 will 
make the number 56 ? 

32. What number taken from 4 times ? of 28 will 
make the number 40 ? 

33. What number added to 5 times 4 of 63 will 
make 67 ? 


78 REVIEW. 


LESSON XXXVI. 

62. 1. If 7 is 3 of some number, what is 1 of the 
same number ? 

2. What number is that to which if 2 of itself be 
added, the number will be 48 ? 

Norse. — The number is 3 of itself, and 3 added make 8; there- 
fore 48 is § of the number. 

3. What number is that to which if its half and 
fourth be added, the sum will be 100 ? 

4. A lady, being asked how old she was, answered, 
that, if 4 and 3 of her age were added to her age, it 
would be 99 years ; how old was she ? 

©. 60 is $ of how many times } of 32? 

6. 84 is § of how many times 4 of 22? 

7. 18 is # of how many fifths of 35 ? 

8. 20 is § of how many sevenths of 42? 

9. If 33 pounds of butter last a family 1 week, 
how long will 253 pounds last the same family ? 

10. How many times is 13 contained in 113? 

11. How many times 333 are 6 times 163? 

12. How many times 3 times 2} are 102 ? 

13. A watch-chain cost 48 dollars, and 3 of the 
cost of the chain was 2 of the cost of the watch; 
what was the cost of the watch ? 

14. Paid } of my money for pencils, } for an ac- 
count-book, and 16 cents for India-rubber, and had 
4,as much left as I had in the beginning ; how ane 
had I at first ? 

15. A father left his son a legacy, 1 of which he 
spent in 6 months, and ? of the remainder lasted him 
8 months longer, when he had only 100 dollars re- 
maining ; what sum did his father leave him ? 


REVIEW. 79 


Note. — 100 dollars were } of the remainder, and the remainder 
was # of the original sum. 

16. A and B made an even exchange of horses; by 
the trade A lost 24 dollars, which was 2 of the value 
of the horse which he had at first; what was the 

value of each horse ? 

17. If one man can cut 13 cords of wood in a day, 
how long will it take 8 men to cut the same? 

18. If 3 horses consume 2 of a bushel of oats in 2 
days, how many horses will consume 8} bushels in 
the same time ? 

19. 2 of 86 is 4 of how Ds tenths of 20 ? 

Nore. — 2 of 36 is 8, 8 is 4 of 14, 3 i of 20 is 2, and 2 is contained 
in 14, 7 tae Then 2 of 36 is 4 of {1 of 20. 

20. 2 of 44 18 

21. 4 of 80 is $ of how many ninths of 54? 

22. 4 of 50 is & of how many sixths of 54? 

23. A farmer, having sold a load of wood for $7}, 
spent # of the money for tea, at ? of a dollar a pound, 
and the balance for coffee, at 3} of a dollar a pound; 
how many pounds of each did he obtain ? 

24. 8 dozen of eggs, at 4 of a dollar a dozen, will 
pay for how many yards of cloth, at 7 of a dollar a 
yard ? 

25. What is a fraction? The denominator of a 
fraction? The numerator ? 

26. What is a proper fraction? An improper frac- 
tion ? 

27. What are the terms of a fraction? When is 
a fraction in its lowest terms? When have fractions 
a common denominator ? 


of rae many sevenths of 35? 


op coh HBO 
Col colex coo clro 6 


80 DENOMINATE NUMBERS. 


DENOMINATE NUMBERS. 


——_—}>-_— 


LESSON XXXVII. 
63. What is United States Money? United 


States Money is the legal currency of the United 
States. 


TABLE. 


10 mills are 1 cent. 

10 cents, 1 dime. 
10 dimes, 1 dollar. 
10 dollars, 1 eagle. 


Norr. — Dollars and cents, when written together, are distin- 
guished by a point (.), called the decimal point, between the dollars 
and cents. 

Thus, $5.10 is read five dollars ten cents, and $10.03 is read ten dol- 
lars three cents. 


64. 1. How many mills are there in 9 cents ? 

2. How many cents are there in 80 mills ? 

3. How many cents in 1 dime? In 8dimes? In 
T dimes? Init dimes? In 14 dimes ? 

4. How many dimes in 10 cents? In 20 cents? 
In 90 cents? In 100 cents? In 110 cents? In 150 
cents ? 

5. How many dimes in 43 cents ? 

6. How many dollars in 1 eagle? In 2 eagles? 
In 7 eagles? In 11 eagles? 


DENOMINATE NUMBERS. 81 


7. How many eagles in 10 dollars? In 20 dollars? 
In 70 dollars? In 120 dollars? | 

8. How many cents in $1? In $2? In $5? In 
$9 ? 

9. How many dollars in 100 cents? In 200 cents ? 
In 700 cents? In 900 cents? 

10. At 5 mills a yard, how many cents will 20 
yards of tape cost ? 


LESSON XXXVIII. 


65. What are 
Troy weights ? 

Troy Weights 
are those used for 
weighing gold, sil- 
ver, and jewels. | 


TABLE. 
24 grains (gr.) are 1 pennyweight, pwt. 
20 penny weights, 1 ounce, OZ. 
12 ounces, 1 pound, Ib. 


66. 1. How many grains in 1 pennyweight? In 
2 pennyweights ? In 4 pennyweights ? 

2. How many pennyweights in 24 grains? In 48 
grains? In 96 grains ? 

3. How many pennyweights in 1 ounce? In 2 


ounces? In 5 ounces? 
6 


82, DENOMINATE NUMBERS. 


4. How many ounces in 20 pennyweights? In 40 
pennyweights? In 100 pennyweights ? - 

5. How many ounces in 1 pound? In 2 pounds? 
In 5 pounds? In 9 pounds? In10 pounds? In 12 
pounds? 

6. How many pounds in 12 ounces? In 36 ounces? 
In 60 ounces? In 144 ounces ? 

7. In 8 oz. 10 pwt. how many pennyweights ? 

8. In 6 lb. 7 oz. how many ounces ? 

9. At 6 cents a pennyweight, what will 40z. 10 pwt. 
of silver cost ? 

10. At 9 dimes a pennyweight, what must be paid 
for 1 oz. 5 pwt. of gold? 


LESSON XXXIX. 


67. What are avoirdupois weights? Avoitr- 
dupois Weights are those used for weighing all 
articles estimated by weight except gold, silver, and 
jewels. 


TABLE. 

16 drams (dr.) are 1 ounce, OZ. 
16 ounces, 1 pound, lb. 
100 pounds, 1 hundred-weight, cwt. 
20 hundred-weight, 1 ton, fie 


68. 1: How many ounces in 1 pound? In 2 
pounds? In 5 pounds? In 10 pounds? In 82 
drams ? 

2. How many pounds in 16 ounces? In 32 ounces? 
In 80 ounces? In 96 ounces ? 

3. How many drams in 2 ounces? In 3 pounds? 
In 1 ounce 8 drams ? 


DENOMINATE NUMBERS. 83 


4, How many ounces in 32 drams? In 40 drams? 

5. What will 8 ounces of candy cost at 2 cents per 
ounce? At 34 cents per ounce ? 

6. How many hundred-weight in 2 tons? In 3 
tons? In5tons? In 6 tons? 

7. How many tons in 20 hundred-weight? In 40 
hundred-weight? In 80 hundred-weight? In 60 
hundred-weight ? 

8. What cost 4 hundred-weight of sugar, at 9 cents 
a pound? At 8 cents a pound ? 

9. What cost 6 tons of bone-dust, at 2 dollars a 
hundred-weight ? 

10. How many pounds in 1 ewt. 18 lbs. ? 

11. How much will 2 ewt. of beef cost, at 10 cents 
a pound ? . 

12. If 5 ewt. of guano cost 15 dollars, how much 
will 3 tons cost ? 

13. How much will 3 of a hundred weight of salt 
cost at 5 cents a pound ? 

14. How much will } a ton of pork cost at 10 dol- 
lars a hundred-weight ? 

15. If 6 ounces of an article cost 12 cents, what 
will 2 pounds of it cost ? 

16. How much will 2 tons of coal cost at $ of a 
dollar a hundred-weight ? - 

17. How much will 3 hundred-weight of fish cost 
at 6 cents a pound ? 

18. How many tons of coal at 6 dollars a ton can 
be bought for 57 dollars ? 

19. How many hundred-weight of sugar at 9 cents 
a pound can be bought for 36 dollars ? 


84 DENOMINATE NUMBERS. 


LESSON XL. 


oa 


ANN 
iin Wit 
Ws 
AY 


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Mii MN Hl 
i ( a 


SS) 
es aes 
cz = 


ANA 


a 
=~ Lh 


AM 


ms 
rm 


ex 


GPL 


69. What are linear measures? Linear 


Measures are those used in measuring distances, 
and the dimensions of articles. 5 


TABLE.. 

12 inches (in.) are 1 foot, ft. 
3 feet, 1 yard, yd. 
54 yards or 164 feet, 1 rod, rd. 

320 rods, 1 mile, m. 
Also : 
40 rods are 1 furlong, fur. 

8 furlongs, 1 mile, m. 


Nore. — In measuring cloth and other Woven fabrics, the linear 
yard is divided into halves, quarters, eighths, and sixteenths or nails. 


70. 1. How many inches in 1 foot? In 5 feet? 
In 7 feet? In 10 feet? In 12 feet? 


2. How many feet in 24 inches? In 36 inches ? 


DENOMINATE NUMBERS. 85 


3. How many feet in 2 yards ? In 11 yards? In 
15 yards? In 20 yards? 

4. How many yards in 6 feet? In 12 feet? In 18 
feet ? In 24 feet ? 

5. How many rods in 1 furlong? In 3 EOD 
In 7 furlongs? In 1 mile? 

6. How many furlongs in 40 rods? In 120 rods? 
In 160 rods? 

7. How many furlongs in 1 mile? In 8 miles? 
In 10 miles? In 12 miles? 

8. How many miles in 16 furlongs? In 24 fur- 
longs?’ In 40 furlongs? In 96 furlongs ? 

9. How many nails in 2 quarters? In 3 quarters ? 
In 5 quarters ? 

10. How many quarters in 12 nails? In 16 nails? 
In 20 nails? In 24 nails? 

11. How many quarters in 1 yard? In 4 yards? 
In 12 yards? In 20 yards.? 

12. How many yards in 4 quarters? In 20 quar- 
ters? In 80 quarters? In 100 quarters ? 

13.. How many nails in 3 yards 3 quarters 1 nail? 

14. How many quarters in 5 yards 3 quarters ? 

15. If 5 nails of cloth cost 25 cents, what will 
cost 5 yards ? 

16. How many inches in 2 yards 2 feet 6 inches ? 
In 1 yard 2 feet 5 inches. 

17. How many rods in } of a mile? In } of a 
mile? 

18. How many yards in 8 rods? In 5 rods? 

19. In 33 feet how many yar ds? In 66 feet how 
many yards ? 


86 DENOMINATE NUMBERS. 


LESSON XLI. 
_ 71. What is a square? A square is a figure 
having four equal straight sides and four equal cor- 
ners or angles. 


72. What are surface or square measures? S$207°~ 
face or Square Measures are those used in 
estimating surfaces. 


TABLE. 
144 square inches (sq. in.) are 1 square foot, sq. ft. 
9 square feet, 1 square yard sq. yd. 
304 square yards, 1 square rod, sq. rd. 
160 square rods, l,acre, A. 
640 square acres, 1 square mile, sq. m. 


73. 1. How many square inches 
| | in 1 square foot? In 1 twelfth of 
a square foot ? 

2. How many square feet in 1 

square yard? In 8 square yards? 

| In 7 square yards? In 8 square 
yards? In 9 square yards? 

3. How many square yards in 9 
square feet? In 86 square feet? In 81 square 
feet ? 

4. How many square rods in 1 rood? In 3 roods? 
In 7 roods ? 

5. How many roods in 80 square rods? In 120 
square rods? In 160 square rods ? 

6. How many square rods in 1 fourth of an acre? 
In 1 half of an acre ? : 

7. How many square rods in a field 12 rods long 
and 9 rods wide ? ; 


1 Square Inch. 


DENOMINATE NUMBERS. ST 


LESSON XLII. 
74. What is a cube? A Cwbe is a body bounded 


by six square and equal sides or faces. 

75. What are solid or cubic measures? Solid 
or Cubic Measures are those used in measuring 
things having length, breadth, and height or depth. 


Nore. — The dimensions are determined by Linear Measure. The 
contents by Cubic Measure. 


TABLE. 
1728 cubic inches (cu. in.) are 1 cubic foot. cu. ft. 
27 cubic feet, 1 cubic yard. cu. yd. 
128 cubic feet, 1 cord. Cc. 
_ Also: 
16 cubic feet, 1 cord foot. _—_cd. ft. 
8 cord feet, 1 cord. ek 


76. 1. How many cu- 3 
bic inches in 1 cubic foot ? — 
2. How many cubic | 
yards in 27 cubic feet ? : 
In 54 cubic feet ? In 81 yi. 
cubic feet ? = 
3. If 40 cubic feet are | 
1 ton of timber, how many = 
cubic feet are in 2 tons of 
timber? In 8 tons of 
timber? In 5 tons of timber ? 
4, How many tons in 80 cubic feet of timber? In 
120 cubic feet ? In 160 cubic feet ? 
o. How many cord feet in 2 cords of wood? In 5 
cords? In 9 cords? 


B= 


1 Cubic Inch. 


88 DENOMINATE NUMBERS. 


6. How many cords in 16 cord feet? In 24 cord 
feet? In 80 cord feet ? 

T. How many cubic feet in 1 cord of wood ? 

8. What cost 5 cords of wood, if 4 cord feet cost 
$3 ? | 

9. What cost 2 tons 20 cubic feet of timber, at 
$1 for 4 cubic feet ? - 


LESSON XLIII. 


dl 


Ae 


ey =i ) 
APUART GALLON 


wine sft 
0 


Cary CK, 


¢7. What are liquid measures? Liquid Meas- 
wres are those used in measuring all kinds of 
liquids. 


TABLE. 
4 gills (gi.) are pint. pt. 
2 pints, 1 quart. qt. 
4 quarts, 1 gallon. gal. 


78. 1. How many gills in 4 pints? In 8 pints? 
In 12 pints? In 15 pints? | 


DENOMINATE NUMBERS. 89 


2. How many pints in 8 gills? In 16 gills? In 
32 gills? In 36 gills ? 

3. How many pints in 4 quarts? In 6 quarts? In 
9 quarts? In 12 quarts ? 

4. How many quarts in 3 gallons? In 8 gallons? 
In 12 gallons? In 15 gallons ? 

5. How many gills in 1 quart? In 1 gallon? 

6. How many pints in 1 gallon? In 2 gallons? 
In 3 gallons ? 

7. At 15 cents a quart, what will 1 gallon of mo- 
lasses cost ? 

8. What cost 8 gallons of vinegar, at 5 cents a 
quart? At 10 cents? 

9. If 2 quarts of oil cost 48 cents, what cost 1 
quart? pint? 1 gill? 

10. If 2 gills of molasses cost 4 cents, how much 
will 1 gallon cost ? 

11. If 3 quarts of oil cost 60 cents, what cost 3 
gallons and 8 quarts ? 

12. How many gills in 2 quarts and 1 pint? 

13. When 5 gallons of burning-fluid can be bought 
for 8 dollars, what cost T gallons ? 


LESSON XLIV. 


- 9, What are dry measures? Dry Measures 
are those used in measuring such dry articles as 
grain, fruit, roots, coal, ete. 


TABLE. 
2 pints (pt.) are 1 quart. qt. 
8 quarts, 1 peck. pk. 


4 pecks, ~ 1 bushel. bu. 


90 DENOMINATE NUMBERS. 


80. 1. How many pints in 4 quarts? In 6 quarts? 
In 10 quarts? In 11 quarts? 

2. How many quarts in 12 pints? In 18 pints? 
In 20 pints? In 30 pints ? 

3. How many quarts in 4 pecks? In 8 pecks? 

4. How many pecks in 16 quarts? In 82 quarts? 
In 64 quarts? In 40 quarts ? 

5. How many pecks in 4 bushels? In 5 bushels ? 
In 9 bushels? In 6 bushels ? 

6. How many bushels in 12 pecks? In 82 pecks? 
In 48 pecks? In 50 pecks? 

7. What costs 1 bushel of corn, at 8 cents a quart ? 
At 2 cents ? 

8. What cost 2 pecks of cherries, at 4 cents a 
pint? At 5 cents? 

9. How many quarts in 2 bushels? In 3 bushels? 
In 10 bushels ? 

10. How many quarts in 2 bu. 3 pk. 4 qt.? 

11. If 3 pints of cherries cost 15 cents, what will 
1 bushel cost ? 


LESSON XLV. 


81. What is time ? Téme is measured portion 
of duration. 


TABLE. 
60 seconds (sec.) are 1 minute, m. 
60 minutes, 1 hour, h. 
24 hours, 1 day, d. 
365 days, ‘I common year, ¢. y. 
366 days, 1 leap year, Ly. 


DENOMINATE NUMBERS. 91 


Also : 
7 days are 1 week, wk. 
12 calendar months 1 year, y: 
100 years, 1 century. 


82. 1. How many seconds in 2 minutes? In 38 

minutes? In 4 minutes? 

. How many minutes in 120 seconds ? 

. How many minutes in 2 hours? In 4 hours. 
. How many hours in 2 days? In 3 days? 

. How many days in 48 hours? In 72 hours ? 

. How many days in 4 weeks? In 6 weeks? 
In 9 weeks? In 10 weeks ? 

7. How many weeks in 14 days? In 56 days? 
In 65 days? In 84 days? 

8. How many months in 6 years? In 10 years ? 

9. If you can read 6 pages in 12 minutes, how 
many hours will it take you to read 10 times as many 
pages ? 

10. Charles is 8 years 3 months old, and John is 7 
years 10 months ; how many months older is Charles 
than John ? 

11. Ifa man can earn 60 dollars in 3 months, in 
how many months can he earn 100 dollars ? 

12. If in 5 hours 8 pairs of shoes can be made, in 
how many days, of 10 hours each, can 24 pairs be 
made ? 

13. If a ship sails 5 miles an hour, how far will it 
sail in a week ? 

14. If a man can earn 1 cent a minute, how 
much can he earn in a day, when he labors 8 hours 
a day? 


So Or Re CO bb 


92 DENOMINATE NUMBERS. 


LESSON XLVI. 


S83. Counting. S4. Paper. 
12 ones are 1 dozen. 24 sheets are 1 quire. 
12 dozen, 1 gross. 20 quires, 1 ream. 


85. Capacity. 


56 pounds of rye or corn are 1 bushel. 


60 pounds of wheat, 1 bushel. 
100 pounds of grain or flour, 1 cental. 
196 pounds of flour, 1 barrel. 
200 pounds of beef or pork, 1 barrel. 


86. 1. How many units in 4 dozen? In 8 dozen ? 

2. What cost 4 dozen peaches, at 2 cents apiece ? 

3. What cost 1 gross of writing-books, at 10 cents 
each ? 

4. How many centals in 600 pounds? In 800 
pounds? In 1000 pounds? 

5. What cost 1 cental of flour at 5 cents a pound ? 

6. What cost 1 gross of pens, at 5 cents a dozen? 

7. What cost 1 ream of paper at 10 cents a quire? 
At 12 cents ? 

8. What costs 1 quire of paper, when 3 sheets can 
be bought for 2 cents ? 

9. At $7 a hundred-weight, what cost 1 barrel of 
beef? 3 barrels ? 

10. Bought a barrel of pork at 12 cents a pound, 
and sold it at $15 a hundred-weight ; how much was 
made by the sale ? 

11. Bought wheat at 3 cents a Ae and sold it 
at $2 a bushel ; how much was made on a bushel ? 


REVIEW. 93 


12. Bought beef at $16 a barrel, and sold it at 
10 cents a pound; how much was made on a barrel ? 

13. What cost 1 ream of paper, at 2 sheets for 
a cent ? 

14. How many score in 5 dozen? In 10 dozen? 
In 15 dozen ? wer 

DEFINITIONS. 

87. What is a denomination? A Denomina- 
tion is the name of a unit expressing a measure. 

88. What isadenominate number? A Denom- 
inmate Number is a number expressing one or 
more denominations. 


Thus, 5 dollars, 5 pounds 6 ounces, are each a denominate number. 


REVIEW. 


——4— 


LESSON XLVII. 
89. 1. What part of 1 peck is 5 quarts? 


So.urion. —1 peck is 8 quarts, 1 quart is 1, and 5 quarts are § 
of 8 quarts. 


2. What part of 1 dollar is 3 dimes ? 

3. What part of 1 pound avoirdupois is 5 ounces? 
Is 8 ounces ? 

4. What part of 2 yards is 2 feet? Is 5 feet? 
. What part of 2 dimes is 18 cents ? 
. What part of 1 week 4 days is 5 days ? 
. What part of 5 bushels is 3 pecks 6 quarts ? 
. What part of 10 pounds is 4 pounds 12 ounces ? 
. What part of 3 yards 8 quarters is 3 quarters 
3 nails ? 


co CO “I os 


94 REVIEW. 


10. What part of 1 rod is 11 feet? Is 22 feet ? 

11. What part of 8 yards is 8 quarters? Is 1 
yard 2 quarters ? | 

12. At $3} a week, how much must 3 days’ -board 
cost ? : 

13. At 60 cents a pound, how much must 12 ounces 
of tea cost ? 

14. At $6 per cord, how much must 7 cord feet of 
wood cost ? 

15. At $25 per ton, how much must 9 hundred- 
weight of hay cost ? 

16. At 64 cents per gallon, how much must be paid 
for 3 quarts 1 pint of molasses ? 

17. If a steamer goes at the rate of 10 miles per 
hour, how far will it go in 3 of a day ? 

18. When silver is worth $1} per ounce, how much 
is that a pennyweight ? 

19. At $20 per ton, what will 1 ton 5 hundred 50 
pounds of hay cost ? 

20. At 50 cents per yard, what will 2 yards 1 
quarter 2 nails of flannel cost? 

21. John worked 2 hours 30 minutes, Henry 3 
hours 15 minutes, and James 1 hour 20 minutes, 
how long did they all work ? 

22. A farmer had 8 bushels 1 peck of apples and 
sold of them 3 bushels 3 pecks, how many had he 
then left ? 

23. I have 5 cans. Each will hold.1 gallon 3 
quarts ; how much will they all hold ? 

24. If 18 pounds 8 ounces of raisins should be di- 
vided equally among 6 persons, how many pounds 
would each receive ? 


io) 
i 


REVIEW. 


LESSON XLVIII. 


90. 1. What part of a pint is 7s of a ener ? 


SotuTion. — 1 gallon is 4 quarts; ;4, of a gallon is 54, of 4 quarts, 
which is ;4, or } of a quart; and 1 quart is 2 pints; 4 of a. quart is 


12 


4 of 2 pints, or 2 of a pint. 


CO 00 I CT 09 PO 


10. 
1A 
12. 


. What part of. an inch is 25 of a yates ¢ 

. What part of a Denis meg is gg of an ounce ? 
. What part of a rod is abo of a mile? 

. What part of a day is ~ of a week? 


What part of a gill is 25 of a gallon? 
What part of a aeaete is 3 of a day? 


. What part of a yard is 335 of an inch ? 


. What part of a ton is 1} of a pound? 
What part of a aaa pes is 3 of a pint ? 
What part of a pound is \ of a pennyweight ? 
What is the value of 3 2 of a pound Troy ? 


SoLuTION. — 1 pound is 12 ounces; 3 of a pound is 2 of 12 


8 


ounces, or 44 ounces; and since 1 ounce is 20 pennyweights, 4 of 
an ounce is 4 of 20 pennyweights, or 10 pennyweights. The value 
of 2 of a pound Troy is 4 ounces 10 pennyweights. 


13. 
. What is the value of 3 of a gallon? 

. What is the value of # of a bushel ? 

. What is the value of 3%; of a ton weight ? 

. What is the value of 33, of a week? 

. What is the value of 3 of a day in hours ? 

. What is the value of 8 of a gallon in pints ? 

. What part of a hundred-weight is 2, of a ton? 
. What is a denomination? A denominate num- 


What is the value of 8 of a yard? 


96 PERCENTAGE. 


PERCENTAGE. 


——— 


LESSON XLIX. 
91. 1. How much is y},5 of $100? Of 100 cents? 
2. How much is z},5 of $2? 


SoLution. — $2 are 200 cents, ;4, of 200 cents is 2 cents. 


3. How much is +4, of $4? Of $7? Of $13? 
Of $64? 

4. How much is ;3, of $200? Of $300? Of $500? 
Of $800 ? 

5. How much is y4y of $150? Of $250? Of $450? 
Of $750? 

6. How much is 72,5 of $100? Of $200? Of $1? 
Of 1 dime or 100 mills? 

T. How much is 72, of $10? 

SoLuTion. — $10 are 100 dimes; ;2, of 100 dimes are 2 dimes, 
or 20 cents. 

8. How much is 72, of $30? Of $50? Of $48? 
Of $64? 

9. How much is 73, of $36? Of $45? Of $28? 

10. How much is +8, of 820 bushels ? 


SOLUTION. — rh of 320 hnahae is B20 of a bushel, or 3,20, 
which is 34 bushels; and —5_ is 5 times 31 bushels, or 16 meth 


160 


11. How much is +4, 0 of 225 tons ? 

12. How much is ,8, of 100 pounds? Of 150 
pounds? Of 360 panned ? 

13. How much is ,7, of 420 yards? 

14. How much is +8, a 250 dollars ? 

15. How much is ,8, of $150? Of $75? Of 
$300? Of 600? : 


PERCENTAGE. 97 


DEFINITIONS. 

92, What is meant by any per cent. of a number ? 
Any Per cent. of a number is so many hundredths 
of that number. 

953, What is percentage? Percentage is the 
process of computing in hundredths; and the per- 
centage is the number obtained by taking any per 
cent. of a number. 

94. What is the rate per cent.? The Rate is 
the number of hundredths denoted by the per cent. 

95, What is the base of percentage? The Base 
of percentage is the number upon which the per cent. 
is computed, 


LESSON L. 


96. 1. How much is 5 per cent. of $100? Of 
$90? Of $150? 

2. How much is 10 per cent. of $100? Of $1, or 
100 cents? Of $10? Of $111? 

3. How much is 20 per cent. of $200? Of $1, or 
100 cents? Of $201? 

4. How much is 15 per cent. of $1000? Of $1500? 
Of $2500 ? 

5. How much is 9 per cent. of 320 barrels ? 

6. A man divides his property among his four sons ; 
to the youngest he gives 15 per cent., to the next 20 
per cent., to the second son 30 per cent., and the re- 
mainder to the eldest ; what per cent. did he give the 
eldest ? 

7. If I give away 25 per cent. of my money to A, 

7 


98 | PERCENTAGE. 


and 20 per cent. to B, and lend. 55 per cent. to my 
brother, how much do T have left ? 

8. Bought a drove of cattle; in the first town I 
passed through, I sold 25 per cent. of them, and af- 
terwards lost 8 per cent.; what per cent. of the drove 
had I then left ? 

9. If I draw 23 per cent. of my money out of the 
bank where it is placed, how much remains there ? 

10. If I borrow $70, and pay 6 per cent. a year for 
the use of it, how much do I pay in 6 years? 

11. How much is 4 times 7 per cent. of $50? 

12. How much is 8 times 6 per cent. of $80? 

13. How much is 9 times 5 per cent. of $60? 

14. How much is 3 per cent. of $100? Of $10? 
Of $1? Of 1 dime? 

15. How much is ? per cent. of $200? Of $20? 
Of $12? Of $1? 

16. How much is 53 times 3 per cent. of 150 
pounds ? 

17. How much is 6 times 5 per cent. of 225 vortlet ? 
Of 150 yards? 

18. What sum is allowed for selling goods to the 
amount of $500, at 24} per cent. commission ? 

19. A city broker exchanged $400 on a country 
bank, at $ per cent.; what did he get for his trouble? 

20. A man having $200 in uncurrent bank-bills, 
paid 11 per cent. to have them exchanged for current 
money; how much did he pay ? 

21. How much is 5 times 6 per cent. of $150 ? 

22. How much is 44 times 6 per cent. of 200? 10 
times 54 per cent. of 100? | 


PERCENTAGE. 99 


LESSON LI. 
97. 1. What fractional part of anything is 10 per 


cent. of it? 

SoLutTion.—10 per cent. is 1° which, reduced to its lowest 
terms, is 54. 

2. What fractional part of anything is 12} per 
cent. of it? 

So.urion. — 123 = 28; $ of 1 per cent. is } of 54,, or sty, 
and 25 of 1 per cent. is 25 times g}5, or 4. 

3. What fractional part of a quantity is 20 per 
cent. of it? 25 per cent.? 50 per cent.? 56 per 
cent.? 75 per cent.? 40 per cent.? 80 per cent. ? 
15 per cent.? 60 per cent. ? 

4. What fractional part of a quantity is 333 per 
cent. of it? 82 per cent.? 3874 per cent.? 162 per. 
cent.? 662 per cent.? 624 percent.? 873 per cent. ? 
61 per cent. ? 

5. What fraction is 4 times 6 per cent. ? 

6. What fraction is 54 times 8 per cent. ? 

7. What part of a ton is 24 per cent. of 75 per 
cent. ? 


SoLurTion. — = zi, and 8 of 75 per cent. is 18 per cent. 


24 
100 
8. What part of a drove of sheep is 20 per cent. of 
80 per cent. of it? 
9. What part of a ship is 25 per cent. of 50 per 
cent. of it? 
10. What per cent. of anything is } of it? 
11. How many per cent. of anything is } of it ? 
12. How many per cent. of anything is 3 of it? 
13. A man lost 4 of his money ; what per cent. did 
he lose ? 


100 PERCENTAGE. 


14. If a man pays 3 of his yearly income for 
board, what per cent. does he have left for other pur- 
poses ? . 

15. How many per cent. of a quantity is 3 of it? 
Zof it? ¢of it? ¥ of it? Zofit? 2ofit? ¢ of 
it? Zofit? Profit? fs of it? tofzofit? 4 of 
4 of it? 

16. In a certain school,. 20 per cent. are in the first 
class, 2 of the remainder in the second class, and the 
rest in the third class, which has two equal divisions ; 
what fractional part of the school is in each division? 

17. What per cent. of 24 is 6? 

18. What per cent. of 10 is 2? Of 50 is 5? 

19. What per cent. of 251s 5? 10? 8? 20? 

20. What per cent. of 42is 7? 14? 21? 35? 

21. 7 is what per cent. of 14? Of 28? Of 49? 
Of 70? Of 140? 

22. $25 is twice what per cent. of $150 ? 

23. 4 is what per cent. of 123? : 

24. tis what per cent. of 4? Of 12? Of 20? 

25. 1 is what per cent. of 23? Of 53? Of 61? 

26. 2 of # is what per cent. of 4 of 12? 

27. 4 of 16 per cent. is what per cent. of 24 per 
cent.? Of 64 per cent. ? 

28. 4 of 15 per cent. is what per cent. of 18 per 
cent.? Of 380 per cent. ? 

29. 2 of 16 per cent. is what per cent. of .24 per 
cent.? Of 72 per cent. ? 

30. If a miller takes out 4 quarts for every bushel 
he grinds, what per cent. toll does he take ? 

31. If of a hogshead of sugar } is sold, and of the 


PERCENTAGE. 101 


remainder 4 is rendered unsalable, what per cent. is 
the remainder ? 

82. ¢ of 41s what per cent. of ?? 

33. Sold, from a box of sugar containing 150 
pounds, at one time 20 pounds, and at another time 
30 pounds; what per cent. of the whole was sold ? 

34, Of 120 yards of cloth there have been sold 
108 yards ; what per cent. of the whole remains un- 
sold ? 

35. 25 per cent. of 834 per cent. is what per cent. 
of 162 per cent. ? 

36. 33% per cent. of 80 per cent. is what per cent. 
of 123 per cent. of 160 per cent. ? 

37. What per cent. of anything is 50 per cent. of 
25 per cent. of 80 per cent. of it? 

38. 3 of 100 is what per cent. of 2 of 833? 


LESSON LII. 
98. 1. 12 is 6 per cent. of what number ? 


SoLution. — Since 6 per cent. of some number is 12, 1 per cent. 
of that number is } of 12, or 2, and 100 per cent. or the number 
itself, is 100 times 2, or 200. 

2. 15 is 10 per cent. of what number ? 

SoLution. — 10 is 1: since 1 of some number is 15, 19, or 


160 5° 10") 10 > 10? 
the number itself, is 10 times 15, or 150. 


3. 20 is 5 per cent. of what number? 4 per cent. ? 
10 per cent. ? 

4, 141s 12 per cent. of what number? 38 per cent. ? 
15 per cent. ? 

5. tis T per cent. of what number? 6 per cent. ? 
4 per cent. 


102 PERCENTAGE. 


6. 24 is 40 per cent. of what number? 12 per 
cent.? 25 per cent. ? 

7. Sold rye so as to gain 25 cents a bushel, which 
was 20 per cent. of what it cost; what did it cost ? 

8. Paid 80 cents for making a vest, which was 20 
per cent. of the cost of the cloth; what was the cost 
of the cloth? 

9. Bought a horse for $160, which was 20 per cent. 
less than his true value; what was his true value ? 

10. If I buy a carriage for $228, at 24 per cent. 
less than what I can sell it for, what can I sell it 
for? 

11. A sells a lot of dry goods for $60, at 20 per 
cent. above cost; what did the goods cost him ? 

12. A merchant sold a lot of goods for $260, and 
thereby gained 30 per cent. ; what was the cost ? 3 
13. Sold a coat for $7, and ies lost 30 per 

cent. ; what was the cost ? 

14. Sold 2 horses, at $200 ie ; on one there 
was a gain of 20 per cent., and on the other a loss 
of 20 per cent.; was ates a gain, or a loss, on the 
sale of the two, and of how much ? 

15. An apple-woman bought apples at 60 cents a 
hundred, and sold them at 1 cent apiece; how much 
per cent. did she gain ? 

SoLuTion. — Since she bought apples at 60 cents a hundred and 
sold them at 100 cents a hundred, she gained the difference between 
_100 cents and 60 cents, or 40 cents on every 60 cents. As 40 cents are 

$p or 2 of 60 cents, the gain is 2 of 100 per cent. or 662 per cent. 

16. When cloth is bought at $1.20 per yard, and 
sold at $1 per yard, how much per cent. is the 
loss ? 


INTEREST. 103 


17. Bought cloth at 80 cents per yard, and sold it 
at $1 per yard; how much per cent. was gained ? 

18. If a horse be bought for $80, and a cow for 
$25, and each be sold so as to gain 16 per cent., how - 
much is received for them both ? 

Nore. — Either find 16 per cent., or 4, of the cost, and add it to 
the cost; or find 116 per cent., or 29 of the cost. 

19. John Robinson buys a cargo of coal for $525, 
and sells it so as to gain 12 per cent.; for how much 
does he sell it? 

20. Having a house worth $1400, I charge for it 
$93 per month ; how much per cent. a year do I get — 
for it? 


INTEREST. 


NERS 


LESSON LIII. 


99. 1. What is the allowance for the use of $1 or 
100 cents for 2 years at a yearly rate of 6 per cent. ? 


Sotution. — The allowance for the use of $1 or 100 cents for 1 
year at 6 per cent. is 6 cents, for 2 years it must be 2 times 6 cents, or 
12 cents. 


2. What is the allowance for the use of $1 for 3 
years at a yearly rate of six per cent.? For 4 years ? 
For 10 years ? 

3. What is the allowance for the use of $1 for 2 
years, at a yearly rate of 4 per cent.? For 5 years ? 
For 8 years ? 

4. What is the allowance for the use of $10 for 1 
year, at 5 per cent. ? 


104 INTEREST. 


So.ution. — The allowance for the use of $1 for 1 year is 5 cents; 
hence, the allowance for the use of $10 for 1 year must be 10 times 5 
cents, or 50 cents. Or, 

The allowance at 5 per cent is 35, or gt, of $10; gy of $10 is $4 
or 50 cents. 


5. What is the allowance for the use of $2 for 1 
year, at 6 percent.? At 5 per cent.? At 8 per 
cent. ? 

6. What is the allowance for the use of $4 for 1 
year, at 6 per cent.? Of $5? Of $7? Of $10? 

7. What is the allowance for the use of $75 for 1 
year, at 8 per cent.? At 10 percent.? At 12 per 
cent. ? i . 3 

8. What is the allowance for the use of $125 for 1 
year, at 6 per cent.? At 5 per cent.? At 7. per 
cent. ? 

9. What is the allowance for the use of $50 for 1 
year, at 6 per cent.? At 4 per cent.? At 8 per 
cent. ? 

10. What is the allowance for the use of $5 for 4 
years, at 6 per cent. ? 


SotutTion. — The allowance for the use of $5 for one year at 6 


per cent. is ,8, of $5, which is $0.30; hence, for 4 years it must be 4 


times $0.30, or $1.20. 


11. What is the allowance for the use of $4 for 2 
years, at 6 per cent.? Of $6? Of $38? 

12. What is the allowance for the use of $10 for 
5 years, at 4 per cent.? At 3 percent.? At 5 per 
cent. ? 

13. What is the allowance for the use of $25 for 
6 years, at 6 per cent.? At 8 per cent. ? 


INTEREST. 105 


14. What is the allowance for the use of $10 for 3 
years, at 6 per cent.? Of $12? Of $20? 

15. What is the allowance for the use of $50 for 5 
years, at 6 per cent.? For 4 years ? 

16. What is the allowance for the use of $600 for 
5 years, at 84 per cent.? At 63 per cent.? At 6 
per cent. ? 7 

17. What is the allowance for the use of $400 for 
7% years, at 5 per cent.? At 8percent.? | 

18. What is the allowance for the use of $60 for 7 
years, at 6 per cent.? For 9 years ? 

19. What is the allowance for the use of $240 for 
10 years, at 5 per cent.? At 74 per cent.? At 4 
per cent. ? 

20. What is the allowance for the use of $3 for 3 
years, at 38 per cent. ? Of $33? Of $54? Of $61? 

21. What is the allowance for the use of $15 for 8 
years, at 10 per cent.? At4percent.? At 6 per 
cent. ? 

22. What is the allowance for the use of $100 for 
5 years, at T per cent.? For 6 years? For 7 years? 


DEFINITIONS. 


100, What is interest? Interest is an allow- 
ance paid for the use of money, or value received. 

101. What is the principal? The Principal 
is the sum on interest. 

102, What is the rate of interest ? The Rate of 
interest is the per cent. allowed of the principal for 
one year, or any given time. 

103, What is theamount? The Amount is the 
sum of the principal and interest. 


106 INTEREST. 


LESSON LIV. 


104, 1. What is the interest of $100 for 1 month, 
at 6 per cent. 


So.ution. — The interest of $100 for 1 year at 6 per cent. is $6; 
hence, for 1 month, or =, of a year, it must be 4, of $6, which is $4, 
or 50 cents. 


2. What is the interest of $1 for 1 month, at 6 
per cent.? Of $10? Of $6? Of $8? 

3. What is the interest of $1 for 1 month, at 12 
per cent.? At9percent.? At 8 percent.? AtT 
per cent.? At 4 per cent.? At 5 per cent.? At 
10 per cent.? At 8 per cent. ? | 

4. What is the interest of $60 for 2 months at 6 
per cent.? Of $9? Of $90? 

o. What is the interest of $200 for 1 month, at 6 
per cent.? Of $300 ? Of $3860? Of $420? 

6. What is the interest of $100 for 4 months, at 6 
per cent.? For 5 months? For 6 months? For 8 
months? For 10 months ? 

7. What is the interest of $100 for 6 months, at 7 
per cent.? At 8 per cent.? At 12 per cent.? 

8. What is the interest of $100 for 4 years and 4 
months, at 6 per cent.? Of $200? Of $300? 


Notr.— 4 years 4 months = 44 years, or 13 of a year. 


9. What is the interest of $50 for 4 years and 3 
months, at 4 per cent. ? At 8 per cent. ? 

10. What is the interest of $150 for 6 years anid 8 
months, at 6 per cent.? For 4 years 2 months ? 

11. What is the interest of $468 for 8 years and 4 
months, at 5 per cent.? For 1 year 8 months? 


INTEREST. 107 


12. What is the interest of $625 for 5 years and 6 
months, at 8 per cent. ? 

18. What is the interest of $800 for 1 year and 7 
months, at 8 per cent. ? 

14. What is the interest of $1 for 30 days, allow- © 
ing 30 days to be 1 month, at 6 per cent.? For 60 
days? For 120 days? 

15. What is the interest of $1 for 20 days, or 3 of 
a month, at 6 per cent.? For 40 days? For 90 
days? For 12 days? For 15 days? For 100 
days ? 

16. What is the interest of $60 for 24 days, at T 
per cent.? For 45 days? For 18 days? For 36 
days? For 72 days? 


Notre. — In computing interest, it is customary to regard 30 days 
as 1 month, or ;, of a year. 


17. What is the interest of $10 for 1 day, or = of 
a month, at 6 per cent. ? 

18. What is the interest of $20 for 5 days, at 6 per 
cent.? Forl day? For 3 days? 

19. What is the interest of $1 for 2 days, at 12 per 
cent.? Forlday? For 14 days? 

20. What is the interest of $600 for 2 years, 1 
month, and 18 days, at 5 per cent. ? 

21. What is the interest of $800 for 9 months and 
1f) days, at 9 per cent. ? 

22. What is the interest of $210 for 3 years and 4 
months, at 7 per cent. ? 

23. The interest of $240 for a certain time is $18, 
at 6 per cent., how much is it at 8 per cent. ? 

24. Find the interest of $40 for 4 years and 2 


108 INTEREST. 


months, at 6 per cent. At 4 per cent. At 5 per 
cent. At 7 percent. At 8 per cent. 

25. Find the interest of $10 for 8 months one 12 
days, at 6 per cent. At 4 per cent. At 5 per cent. 
At T per cent. At 8 per cent. 


LESSON LV. 


105. 1. What is the amount of $40 for 2 years, at 
6 per cent. ? 

So.ution. — The interest of $40 for 2 years at 6 per cent. is $4.80, 
and $40 + $4.80 = $44.80, the amount. 

2. What is the amount of $60 for 4 years, at 4 per 
cent. ? 

3. What is the amount of $80 for 8 years, at 5 per 
cent.? For 4 years ? 

4. What is the amount of $100 for 6 years, at 4 per 
cent.? At 6 per cent. ? 

5. What is the interest of 870 for 6 years, at 7 per 
cent.? At 5 per cent. ? 

6. What is the amount of $150 for 2 years, at T per 
cent.? For 4 years ? 

7. What is the interest of $100 for 3 years and 4 
months, at 7 per cent. ? 

8. What is the interest of $25 for 6 years and 1 
month, at 6 per cent. ? 

9. What is the interest of $10 for 4 years and 2 
months, at 12 per cent. ? 

10. What is the amount of $150 for 4 years ana 1 
‘month, at 6 per cent. ? 

11. Required the amount of $200 for 2 years and 
2 months, at 4 per cent. 


INTEREST. 109 


12. Required the amount of $145 for 6 years and 3 
months, at 8 per cent. | 

13. Required the amount of $400 for 2 years, 2 
months, and 20 days, at 44 per cent. 

14. What is the amount of $140 for 2 years, 4 
months, and 24 days, at 5 per cent. ? 

‘15. What is the amount of $200 for 2 years, 6 
months, and 15 days, at 6 per cent. ? 

16. What is the interest of $15 for 6 years, 10 
months, and 15 days, at 8 per cent. ? 

17. What is the amount of $360 for 2 years and 1 
month, at 6 per cent. ? 

18. What is the amount of $180 for 6 years and 8 
months, at 10 per cent. ? 

19. What is the amount of $200 for 5 years and 9 
months, at 4 per cent. ? 

20. What is the amount of $140 for 3 years, 1 
month, and 15 days, at 8 per cent. ? 

21. What is the amount of $175 for 4 years and 8 
months, at 6 per cent. ? 

22. What is the amount of $140 for 8 years and 4 
months, at 8 per cent. ? 


LESSON LVI. 
106. 1. If the interest of $300 for 2 years is $48 


what is the rate per cent. ? 

So.Lution. — The interest of $300 for 2 years at 1 per cent. is $6; 
and $48 is as many per cent. as $6 is contained times in $48, or 8 per 
cent. 


2. If the interest of $100 for 4 years is $20, what 
is the rate ? 
3. If the interest of $200 for 2 years is $12, what 


is the rate per cent. ? 


110 | INTEREST. 


4. If the interest of $400 for 3 years is $24, what 
is the rate per cent. ? 

5. If the interest of $25 for 1 year 8 months is $1, 
what is the rate per cent. ? 


SoLuTion. — The interest of $25 for 1 year 8 months, at 1 percent. 
is $,%,; and $1 is as many per cent. as $,5, is contained times in $1, 
or 03 per cent. 


6. If the interest of $150 for 3 years and 4 months 
is $35, what is the rate per cent. ? 

7. If the interest of $50 for 1 year and 3 months is 
$3, what is the rate per cent. ? 

8. If the interest of $75 for 4 years and 2 months 
is $123, what is the rate per cent. ? 

9. A man paid $8 for the use of $48 for 1 year and 
4 months ; what was the rate per cent. ? 

10. John Niles lends Harry Hubbard $30 for 2 
years and 6 months; Harry has to pay at the end of 
the time $36 ; what is the rate per cent. ? 


Note. — The principal, $30, has to be paid back, and is of course 
a part of the $36; the remainder, $6, is the interest, by which the 
rate per cent. is to be found. 


11. A note of $100, being on interest 2 years and 
2 months, amounted to $126; what was the rate per 
cent. ? 


LESSON LVII. 
107, 1. If the interest of $50 at 6 per cent. is $6, 


how long has it been on interest ? 


So.tution. — The interest of $50, for 1 year, at 6 per cent., is $3. 
$6 must then be the interest for as many years as $3 are contained 
times in $6, which are 2. 


2. If the interest of $60, at 2 per cent., is $12, 
how long has it been on interest ? 


INTEREST. 111 


3. How long must $100 be on interest, at 4 per 
cent., to gain $40? 

4, A note of $80, being on interest at 8 per cent., 
amounted to $160 ; how long was it on interest ? 

5. How long must $10 be on interest, at 5 per 
cent., to gain $3. 

6. If the interest of $20, at 4 per cent., is $4, how 
long a time has it been on interest ? 

7. If the interest of $50, at 8 per cent., is $12, 
how long has it been on interest ? 

8. Required the time that $40 must be on interest, 
at 2 per cent., to gain $8. 

9. A gentleman lent $60, at 6 per cent., and re- 
ceived $140 ; how long was it on interest? 

10. A sum of money is on interest at 6 per cent. ; 
how long will it take it to double itself ? 

Nore. — That is, if it gain 6 per cent. a year, how long will it take 
to gain 100 per cent. ? 

11. How long will it take a sum of money to 
double itself, at 9 per cent.? At 18 per cent. ? 

12. A given principal gains 1 of 3 of itself a year; 
how long will it take it to double itself ? 

Nore. — That is, how long will it take to gain 2% of itself? 

13. A given principal gains 2 of 4 of itself a 
year; how long will it take to double itself? To gain 
3 of itself? 1 of itself? 

14. If I loan $1200, at 8 per cent. a year, how 
Jong will it be in gaining $80 ? 

15. If I loan $500, at 7 per cent. a year, how long 
will it be in gaining $350 ?- 


112 INTEREST. 


LESSON LVIII. 


108. 1. What principal in four years at 10 per 
cent., will give $6 interest ? 


So.urion. — The interest equals 4°, or 2 of the principal, which is 
$6. If 2 of the principal is $6, 2, or the princiga® equals 3 of $6, or 


$15. 

2. What principal, in two years, at 4 per cent., 
will give $8 interest ? 

3. What is the principal that, in 4 years, at 8 per 
cent., will give $6 interest ? 

4, What principal, in 5 years, at 6 per cent., will 
give $10 interest ? 

5. What principal is sufficient in 3 years, 2 months, 
and 12 days, at 5 per cent., to gain $64? 

6. What principal is sufficient in two years, at 8 
per cent., to gain $10? 

sh What principal is sufficient in 6 years, at 1 ja 
cent., to gain $20 ? 

8. What principal, in 1 year and 8 months, at 4 
per cent., will gain $5? 

9. What principal, in 6 years and 4 months, at 6 
per cent., will gain $19 ? 

10. What principal is sufficient in 7 years, to gain 
$14, at 7 per cent. ? 

11. The interest on a note for 4 years and 2 
months, at 4 per cent., was $60 ; what was the prin- 
cipal ? 

12. The interest on a note for 5 years and 6 
months, at 6 per cent., was $66; what was the prin- 
cipal ? 


PRESENT WORTH. ES 


PRESENT WORTH. 


one 


LESSON LIX. 


109, 1. What principal, in 4 years, at 5 per cent., 
will amount to $96 ? 


So.utron. — The interest equals ;20,, or 4, of the principal. The 
principal is 3 of itself, hence the amount, which is $96, must be $ of 
the principal. If $96 be 3, then 4 or the principal, must be 8 of $96, 
or $80. 

2. What principal, in 5 years 10 months, at 6 per 
cent., will amount to $9? 

3. What principal, in 5 years at 5 per cent.,.will 
‘amount to $50 ? 

4. What principal, in 6 years at 6 per cent., will 
amount to $136 ? 

5. What principal, in 9 years, at 8 per cent., will 
amount to $172? 

6. What principal, in 5 years, at 10 per cent., will 
amount to 74 ? 

7. What principal, in 1 year, at 4 per cent, will 
amount to $78 ? 

8. What principal put at interest for 10 years, at 
7 per cent., will amount to $85 ? 

9. What principal put at interest for 8 years, at 
Td per cent., will amount to $96 ? 


DEFINITIONS. 
110. What is the present worth of a sum of 
money, payable at a future time without interest ? 


The Present Worth is such a sum as, being placed 
} 8 


114 PRESENT WORTH. 


at interest at the given rate, will amount to the debt 
when it becomes due. 

111, What is discount? Discount is the dif- 
ference between the debt and its present worth. 


LESSON LX. 


112. 1. What is the discount of $84, due in 8 
years, at 5 per cent. ? 


SoLution. — The discount is equal to j4°, or 2 of the present 


worth. The present worth is 3 of itself; hence, the given sum $84 


must be 3 of the present worth, and the present worth $60. The dis- 
count is $84 less $60, or $24. 

2. What is the discount of $100, due in 5 years, 
at 5 per cent. ? 

3. What is the discount of $77, due in 9 years, at 
6 per cent. ? 

4. What is the discount of $66, due in 6} years, 
at 10 per cent. ? 

5. What is the discount of $74, due in 6 years, as 
8 per cent. ? 

6. Whit is the discount of $81, due in 5 years, at 
T per cent. ? 

7. What is the discount of $774, due in 4 years, at 
10 per cent. ? 

8. What is the discount of $57, due in 2 years, at 
7 per cent. ? 

9. What is the discount of $68, due in 10 months, 
at 6 per cent. ? 

10. What is the discount of $81, due in 1 year and 
4 months, at 6 per cent. ? 

11. What is the present worth of $64, due in 5 
years, 7 months, and 6 days, at 5 per cent. ? 


PRESENT WORTH. 115 


12. What is the present worth of $122, due in 100 
days, at 6 per cent. ? 

13. What are the present worth and discount of 
$108, due in 2 years and 11 months, at 12 per cent. ? 

14. What are the present worth and discount of 

! $200, due in 6 years 8 months, at 5 per cent. ? 

15. What are the present worth and discount of 

$50, due in 11 years 1 month and 10 days, at 6 per 


cent. ? 


REVIEW. 


On 


LESSON LXI. 
113. 1. A buys goods, and sells again to B at 10 


per cent. more than he gives; B sells to C, and makes 
20 per cent.; how much per cent. would A make, 
were he to sell to C himself at the same price that B 
receives ? 

Sotution. — As A’s cost is 100 per cent. of itself, B pays 110 per 
cent. of A’s cost, and gives 20 per cent. or 4 of 110 per cent., which is 
22 per cent. of its cost ; hence A, by selling directly to C, would gain 
10 per cent. and 22 per cent. or 32 per cent. 

2. A sells B a watch, and gains 10 per cent.; B 
sells it again to C, and gains 20 per cent.; C pays 
$110; how much did it cost A? 

3. Charles Thompson sells to John Johnson goods 
which he bought for $100, and gains 10 per cent. ; 
he also sells some of the same goods to Peter Wil- 
liams, and gains 30 per cent.; how many dollars 
would Johnson gain if he were to sell all he bought to 


116 REVIEW. 


Williams at the same price that Thompson sells to 
Williams ? 

4, If I sell to A, a retail dealer, and gain 10 per 
cent., and to B, who is one of A’s customers, and 
gain 30 per cent., what per cent. would A gain by 
selling to B at the same price that I sell to B? 

5. If A has 50 per cent. less capital than B, B has 

what per cent. more than A ? 

Sotution. — B’s capital is 100 per cent. of itself, and A’s is 50 per 
cent. less than B’s, A’s must then be 50 per cent. of B’s, and the dif- 
ference between B’s capital and A’s must be 3° of A’s, or once A’s. 
B has 100 per cent. more capital than A. 


6. If A’s capital is 50 per cent. of B’s, B’s is what 
per cent. of A’s? 

7. If James has 50 per cent. more money than 
John, what per cent. has John less than James? 
John’s money is what per cent. of James’s ? 

8. Having a farm of 154 acres, worth $20 an acre, 
I let half of it at 5 per cent. a year on its value, 
and cultivated the other half myself, getting back 
$115 beyond all expenses; is it better for me to let 
my farm or use it myself, and how much difference 
is there ? 

9. Bought a horse for $200, which was 20 per 
cent. less than his worth, and sold him at 95 per 
cent. of his value ; how many dollars were gained ? 

10. If a barrel of flour is bought for § of its mar- 
ket price, and sold for 4 per cent. ae than the 
market price, what per cent. is gained ? 

11. Bought a cargo of flour at 20 per cent. less 
than $7 a barrel, and sold it at 4 per cent. more than 


REVIEW. 117 


$7 a barrel; what per cent. was gained? How many 
dollars were gained on a barrel ? 

12. If Philadelphia had 25 per cent. less popula- 
tion than New York, New York would have how 
many per cent. more than Philadelphia ? 

13. Paid my agent, for the purchase of a horse, 
$168, including five per cent. allowed him for his 
services; what did he pay for the horse ? 

14. One publisher allows his agents 20 per cent. 
of all the money which they receive for his books, 
while another allows his agents to deduct a sum 
equal to 25 per cent. of the amount which they 
remit to him; which terms are most favorable for 
the agents ? 

15. A grocer bought 100 eggs, at 15 cents a dozen, 
but 16 of them proved bad, and he sold the rest at 
18 cents a dozen; how much per cent. did he gain ? 

16. A man gains 20 per cent., in each of three 
years, upon what he had at the beginning of the 
year; how much more has he then than when he 
began ? 


LESSON LXII. 


114. 1. If the interest of $120 for 1 year is $9, 
what is the interest of $60 ? 

SoLutTion. — $60 is 4 of $120. If the interest of $120 is $9, the 
interest of $60 must be 4 of $9, or $44. 

2. If the interest of $400 for 1 year is $24, whew is 
the interest of $100? Of $10? Of $1? 

3. If the interest of $12 for 5 years is $3.60, what 
is the interest of $6? Of $60? Of $3800? 


118 REVIEW. 


4. If the interest of $160 for 2 years is $18, what 
is the interest of $80? Of $40? 

5. If the interest of $280 for 3 years is $46, what 
is the interest of $70? Of $140? 

6. If the interest of $100 for 3 years is $20, what 
will it be for 6 years? For 1 year? For 10 years? 
Tor 4 years ? 

7. If the interest of $180 for 2 years is $23, what 
is it for 8 years? For 7 years? For 9 years? 

8. If the interest of $200 for 3 years is $27, what 
is it. for 1 year? For 1 month? For 4 months? 
For T months? 

9. If the interest of $200 for 1 month is $1, what 
is it for 15 days? For 5 days? For 1 day? 

10. If the interest of $140 for 1 year and 4 months 
is $10, what is it for 8 months? For 4 months? For 
2 months? For 1 month ? | 

11. The interest of $240, at 6 per cent., is $27; 
what is it at 2 per cent.? At 1 per cent. ? | 

12. The interest of $320, at T per cent., is $15; 
what is it at 1 per cent.? At 8 per cent. ? 

13. If the interest of $100 for 8 years is $21, what 
is the rate per cent. ? 

14. In what time would it take $100 to become 
$200 at 5 per cent.? At 8 per cent.? At 10 per 
cent. ? 

15. What principal in 4 years, at 7 per cent. will 
‘amount to $128? 

16. At what rate per cent. interest will $100 gain 
$28 in 4 years? $323 in 5 years? 

17. What is percentage? What is the base of — 
percentage ? 


MISCELLANEOUS. 119 


18. What is interest? What is the principal? 
What is the rate? What is the amount? 

19. What is the present worth of a sum of money? 
What is discount ? 


MISCELLANEOUS. 


LESSON LXIII. 


‘115. 1. Divide a sum of money between A and 
B, giving A $3 as often as you give B $2. What 
share of the money will each receive ? 


Sotution. — As often as A receives $3 and B $2, they both re- 
ceive $3 plus $2, or $5; hence A receives 3 and B 2 of thé money. 


2. If you divide $24 between A and B, by giving 
A $3 as often as you give B $5, how many dollars 
will each receive ?. 

3. Divide $35 between John Wilson and Simon 
Edwards ; how much will each get, if John receives 
$4 as often as Simon receives $3 ? 

4, A man has two sons, to whom he leaves $660, 
to the elder $7 to every $4 he leaves the younger, 
how much does each get ? 

5. I go into partnership with Thomas Gould, and 
pay in $5 of capital to every $4 he pays ; how much 
more do I pay than he? How much less does he 
pay thanI? What share of the whole do I pay, and 
what share does he pay? If we have a profit of 
$63, how much should I receive ¢ How much should 
Gould receive ? 


120 MISCELLANEOUS. 


6. Three men hired a pasture for $36; A put in 
4 oxen, B 3 oxen, and C 5 oxen; how much should 
each pay ? 

T. John Stevens and Samuel Judkins hire a pas- 
ture together; John puts in 8 cows for 2 days, and 
Samuel 4 cows for 6 days; they pay $5. rent; how 
much should each pay ? 


SoLuTION. —3 cows for 2 days would be the same as 2 times 3 
cows, or 6 cows, for 1 day ; and 4 cows for 6 days would be the same 
as 6 times 4 cows, or 24 cows, for 1 day; and both would put in the 
sum of 6 cows, and 24 cows, or 30 cows for 1 day. Hence, John pays 
zy or 4, of $5, which is $1, and Samuel 24, or 4, of $5, which is $4. 

8. Divide 60 into two numbers which shall be to 
each other as 7 to 5. As38to}. As 51 to 2. 

9. Divide 69 into two parts which shall be to each 
other as 2 to ¢. 

10. Two men buy a cask of beer, containing 30 
gallons; one pays $4, and the other $3}; what part 
does each get ? 

11. A gentleman has 8 sons, to whom he gives 63 
cents to celebrate the Fourth of July ; Edward, the 
eldest, has 2 times as much as Robert, the second, 
and 4 times as much as John, the youngest; how 
much does each receive ? 

SoLtutTion. — John’s share is once itself, Edward’s is 4 times John’s 
share, and Robert’s is $ of Edward’s, or 2 times John’s. Hence, the 
whole sum, or 63 cents, is seven times John’s share, and John’s share 
is 9 cents. 

12. Mary had 40 apples; she gave 2 to her school- 
mates, and divided the rest between her two sisters 
and herself, taking only } as many as both her sis- 
ters ; how many did she have for herself ? 


MISCELLANEOUS. BAL 


13. In a granary there is twice as much rye as 
wheat, twice as much wheat as buckwheat, and 4} as 
much barley as rye; there are 125 bushels in all; 
how much of each kind ? 

14. Two men go into partnership ; A puts in $200, 
and B $150, their profits are $32; how much per 
cent. do they gain on their capital, and what is each 
one’s share ? 

15. A, B, and C, enter into partnership; A puts 
ini, B 2, and C the remainder; after a while A 
withdraws his, and the capital is now $480; how 
much does each put in? 

16. C and D hire a pasture together; C pays $12, . 
and D $10; C puts in 6 cows; how many should D 
put in? 

LESSON LXIV. 

116, 1. A cistern is filled by a pipe in 4} hours; 
what part of it is filled in 1 hour? 

2. A man can do } of a piece of work in 1 hour; 
how long will it take him to do the whole ? 

3. Two men together can eat sy of a barrel of 
crackers in 1 day; how long will it take them to eat 
the whole ? 

4. A can do a piece of work in 8 days, and B the 
same work in 12 days; how long will it take them 
both ? 


SoLuTion. — Since A can eh 4 of the work in one day, and B =, 


12 
both can do 7 plus 4 a plus az, OY =; in 1 day; hence it will 


Tp ° i oe 
take them fe many ee s “as the whole work as ,3, are contained 


times in 24, or 44 times. It will take them both 44 days. 


5. Two men can each do ? of a piece of work in 


122 MISCELLANEOUS. 


1 day; how long will it take them both to do the 
whole ? 

6. Two men set out to mow a field; the first can 
mow it in 8 days, and the second in 10; how long 
will it take them both to mow the field ? 

7. A cistern has 3 pipes; the first will fill it in 2 
hours, the second in 3 hours, and the third in 6 hours; 
how long will it take them all to fill it ? 

8. A cistern has 2 pipes; the first will fill it in 2 
hours, and the second will empty it in 3 hours; if- 
both pipes are open, how long will it take to fill the 
cistern ? 

9. A cistern has 4 pipes; the first will fill it in 2 
hours, the second will fill it in 3 hours, the third in 4 
hours, and the fourth will empty it in 2 hours; now, 
if the pipes are all open at the same time, how long 
will it take to fill the cistern ? 

10. A and B together can build a wall in 8 days, 
but with the aid of C they can build it in 5 days; 
how long will it take C to build it alone? 

11. A can reap a certain piece of rye in § of a 
day, B in 2 of a day, and C in 1 day; how long will 
it take them together to finish the piece, aiter O has 
been reaping } of a day ? 

12. Divide 24 into 2 parts which shall be to each 
other as 12 to 3. 

13. Divide 32 into 3 parts which yall be, respec- 
tively, as 24, 13, and 1}. 

14. A and B can do a piece of work in 15 days, 
and B alone in 24 days; how long would it take A 
alone ? 


MISCELLANEOUS. 128 


15. Divide 86 into two parts, of which the larger 
is 54 times as much as the less. 

16. Three men go into partnership ; the first pays 
$7 as often as the second pays $4, and the third $5 as 
often as the second pays $8; they all pay in $540 ; 
how much does each pay ? 

17. Three men, A, B, and C, were to share $400 
in the proportion of 4, 1, and , respectively ; but, as 
C died, it is required to divide the whole sum prop- 
erly between the other two; how much should each 
receive ? 


LESSON LXV. 


117%. 1. If 12 yards of cotton cloth cost $1.60, how 
much will 39 yards cost ? 

2. If 7 horses consume 16 tons of hay a year, how 
many tons do 5 horses consume ? 

3. If 12 men can dig a well in 4 days, in how many 
days can 15 men dig it? 

4, 11 is to 33 as $0.25 is to what sum ? 

d. If 8 and 4 were 12, what, on the same supposi- 
tion, would 2 and 31 be? 

6. If $6 worth of provisions will last 5 men 7 days, 
how long will they last 10 men ? 


SoLutron. —If the provisions last 5 men 7 days, they will last one 
man 5 times 7 days, or 35 days, and they will last 10 men 1, of 35 
days, or 34 days. 

Or: —5 men are 55. or t of 10 men, and the provisions which will 
last 5 men 7 days, will last 10 men 4 of 7 days, or 34 days. 


7. If a barrel of meat will last 12 men 20 days, 


how long will it last 16 men? 36 men? 40 men? 
8. If a barrel of beer last 5 men 16 days, how long 


124 MISCELLANEOUS. 


will it last 8 men? How many men will it last 8 
days ? 

9. If a pole 40 feet high cast a shadow of 25 feet, 
how long a shadow will be cast at the same time by 
a similar pole 16 feet high? How high a pole will 
cast a shadow of 30 feet ? 

10. If I borrow $20 for 8 months, how many dol- 
lars ean I lend for 5 months, in order to return the 
favor? For how many months can I lend $30? 

11. If a man can do a certain piece of work in 5 
days, by laboring 8 hours a day, how many hours a day 
must he labor in order to do it in 4 days? In how 
many days would he do it by laboring 6 hours a day ? 

12. If 8 bushels of grain will last 7 horses 5 days, 

how long will 16 bushels last + horses ? 
- Sorutron. —If 8 bushels of grain will last 7 horses 5 days, 16 
bushels will last them 2 times 5 days, or 10 days; and if they will 
last 7 horses 10 days, they will last 4 horses | of 10 days, or 174 
days. 3 

13. If a ton of hay will last 8 cows 7 days, how long 
will it last 11 cows? 

14. If a ton of hay will last 7 cows 8 days, how 
many cows will it last 14 days ? 

15. If $300 gain $12 in $8 months, what sum 
would it require to gain $8 in 2 months? 

16. If $100 gain $6 in 12 months, how many 
months would it require for $400 to gain $10? 

17. If 40 bushels of oats are sufficient for 5 horses 
6 weeks, how many bushels would it require to supply 
15 horses 8 weeks ? 


18. If 20 oxen eat 4 tons of hay in 30 days, how 


MISCELLANEOUS. 123 


many oxen would it take to eat 12 tons in 60 days? 
In 50 days? In 75 days? 

19. If 7 men can build 8 rods of wall in 4 days, 
how many days would it take 14 men to build 32 rods 
of wall? 40 rods? 80 rods? 


LESSON LXVI. 


118. 1. If 6 men can do the work of 24 women, 
and 4 women do the work of 6 boys, how many men 
can do the work of 18 boys? 

SoLuTion. — Since 6 boys do the work of 4 women, 18 boys will 
do the work of 3 times 4 women, or 12 women; and as 24 women 
do the work of 6 men, 12 women, or 18 boys, will do the work of 
4 of 6 men, or 3 men. 

2. If 5 pounds of cheese are equal in value to 2 
pounds of butter, and 6 pounds of butter to 2 bushels 
of corn, how many pounds of cheese will pay for 4 
bushels of corn ? 

3. If the relative value of oak wood to spruce is as 
2 to 1, and that of spruce to pine as 7 to 8, how many 
cords, composed of spruce and pine in equal parts, will 
equal 10 cords of oak ? 

4. If 3 men can build a boat in 12 days, when 
the days are 12 hours long, how long will it take 5 
men to build the same, when the days are 10 hours 
long ? | 

5. If $150 gain $9 in 12 months, in what time will 
$200 gain $18? 

6. When $24 will purchase 2 of a barrel of flour, 
what part of a barrel can be purchased for $43 ? 

7. If 12 men can reap a field of 4 acres in 8 days, 


126 MISCELLANEOUS. 


by laboring 6 hours a day, how many acres would 6 
men reap in 12 days, by laboring 7 hours a day? 

8. If the interest of $250 for 10 months is $124, 
what is the interest of $450 for 5 months ? 

9. If 2 oxen, or 8 cows, will eat 3 tons of hay in 18 
weeks, how much hay will 6 oxen and 1 cow eat in 9 ~ 
weeks ? 

10. There are in a fort 200 men, with provisions 
sufficient to last 6 months; how many must leave 
after the provisions are half gone, that the remaining 
men shall have just sufficient for 6 months ? 

11. If 8 men can dig a ditch 380 rods long in 20 
days, how long will it take 10 men to dig a ditch 15 
rods long? : 

12. A workman, laboring 10 hours a day, will 
build in 20 days 80 rods of wall; how long will it 
take 10 workmen, laboring 9 hours a day, to build 
45 rods ? | 

13. I can perform a journey in 10 days by traveling 
at the rate of 4 miles an hour; how can I perform | 
it in 8 days, if I travel the same number of hours a 
day ? 

14. If 4 pounds of flour will make 40 four-cent 
loaves of bread, how many six-cent loaves can be 
made from the same quantity ? 

15. If 7 men can do a piece of work in 60 days, 
how many men will be required to do it in 12 days ? 

16. If 8 bushels of wheat cost 10 dollars, how 
much can be bought for 12 dollars ? 

17. A man and a boy can do a piece of work in 12 
days; but without the man the boy could do it in 30 
days. In what time can the man do it alone? 


MISCELLANEOUS. 127 


18. If a 6 cent loaf weighs 15 ounces when flour is $6 
a barrel, what will it weigh when flour is $8 a barrel ? 

19. When 6 men in 4 days can build 80 rods of 
picket fence, how many men will be required to ex- 
tend the same fence 160 rods further in 12 days ? 


LESSON LXVII. 


119. 1. If the difference of two numbers is 30, 
and the greater is 200, what is the less ? 

2. When the difference between two numbers, 
and the greater number are given, how do you find 
the less ? 

3. If the difference of two numbers is 30, and the 
less 150, what is the greater ? 

4. When the difference between two numbers, 
and the less number are given, how do you find the 
greater ? 

5. If the sum of two numbers is 5, and their dif- 
ference is 3, what are the numbers ? 


So.ution. — As the greater number is 3 more than the less, this 
sum, or 5, must be 3 more than twice the less; hence twice the less 
must be 5 —3, or 2, and the less number must be 4 of 2or1. The 
greater number is 1 +3, or 4. 

6. The sum of two numbers is 17, and their differ- 
ence 5. What are they ? 

T. Show that the sum of two numbers added to 
their difference gives twice the greater ? 

8. Show that the difference of two numbers taken 
from their sum gives twice the less. 

9. Divide 65 into two parts, one of which shall be 
19 greater than the other. 


128 MISCELLANEOUS. 


10. Two boys, on counting their money, found that 
the one had $46 more than the other, and together 
they had $54; how much had they each ? 

11. The sum of two numbers is 73, and their dif- 
ference 2}; what are they ? 

12. A man who has 60 sheep and lambs, finds that 
the number of the sheep, less the number of lambs, is 
3 of the flock; how many are there of each kind? 

13. The difference of two numbers is 5, and the 
less number is # of the greater; what are the num- 
bers ? 

14. John Smith gave 9 cents a dozen for apples, 
and had 12 cents left; but, had he paid 12 cents a 
aozen, he would have spent all his money ; how many 


apples did he buy ? 


LESSON LXVIIL 


120. 1. A laborer agreed to work 20 days upon 
the condition that for every day he worked he should 
receive $1.50, but for every day he was idle he should 
forfeit 50 cents; he received $18; how many days did 
he work ? 


So.tution. — Had he worked all the time, he would have received 
20 times $14 or $30; hence, he lost $30 — 18, or $12, by being idle. 
For each day that he was idle, he lost $14 + $4 or $2; he must, then, _ 
have lost as many days as $2 are contained times in $12, or 6 times. 
Tf he lost 6 days, he must have worked the remaining 14 days. 


2. A laborer agreed to work 30 days for $2 a day, 
and for every day he was idle to pay ? of a dollar for 
~ his board; he received $38; how many days was he 
idle ? 

3. A gentleman bought 15 cords of wood, oak and 


MISCELLANEOUS. 129 


pine, for $55; he paid $5 a cord for the oak, and $3 
a cord for the pine; how many cords were there of 
each, and how much did each kind cost ? 

4. A student, having a Bible, a dictionary, and an 
algebra upon his table, was asked the price of each ; 
he answered that his Bible cost twice as much as his 
dictionary, the dictionary cost twice as much as the 
algebra, and that the three books cost $10; what was 
the cost of each book ? 

5. The head of a fish is 9 inches long ;. the tail is 
as long as the head and half the body, and the body 
is as long as the head and tail both ; how long is the 
fish ? 

Sorturion. — The length of the head is 9 inches; the length of the 
tail is 9 inches + 4 the length of the body; and the length of the 
head and tail, or the length of the body is 9 inches + (9 inches + 4 the 
length of the body), or 18 inches + 4 the length of the body. Now, 
since 18 inches + } the length of body, = the whole length of the 
body, 18 inches must be 4 the length of the body; and the whole 
length of the body must be twice 18 inches, or 36 inches. This is $ 


the Jength of the fish, and the whole length must be twice 36 inches, 
or 72 inches. 


6. The head of a fish is 7 inches long; the tail is 
as long as the head and one third of the body, and 
the body is as long as the head and tail both; how 
long is the fish ? 

7. If % of the time to noon is equal to & of the 
time past midnight, what was the hour ? 


SoruTion. — If 3 of the time to noon is equal to § of the time past 


midnight, 3 of the time to noon is equal to 4 of 3, or 55, of the time 
past midnight, and 3, or the time to noon, is equal to 3 times 55, or 
4 of the time past midnight; hence, as the time past midnight is + 
of itself, the time from midnight to noon, or 12 hours, is 3 -> 4, or 4, 


9 


130 MISCELLANEOUS. 


of the time past midnight, and the time past midnight must be ¢ of 


12 hours, or 54. hours. The hour is 20 minutes past 5 o’clock in 
the morning. 

8. A man being asked the time of day, answered 
that 8 times the time to noon was equal to twice the 
time to midnight ; what time was it ? 

Nore. — 12 hours is here the difference of the times instead of their 
sum. 

9. A man being asked what time it was, answered 
that the time past noon was } of the time past mid- 
night ; what time was it ? 

10. A man being asked the time of day, answered 
that the time past noon was equal to 4 of the time 
past midnight; what time was it ? 

11. A man said that 1 of the time past noon was 
equal to 1 of the time to midnight; what was the 
hour ? 

12. A and B start from the same point, and 
travel in the same direction around a square, each 
side of which measures 5 miles; A travels at the 
rate of 41 miles an hour, and B at the rate of 3 
miles an hour; in what time will they be together 
again ? How many miles will each have traveled ? 
How many times will each have been around the 
square ? 

13. A man, being asked the time, answered that 
2 of the time past midnight was equal to ? of the 
time past noon; what was the hour ? 

14. A and B set out to travel round a certain 
island which is 20 miles in circuit; A travels at the 
rate of 5 miles an hour, and B 7 miles an hour; how 
long will it take B to overtake A? 


GENERAL REVIEW. 131 


GENERAL REVIEW. 


—_—~——_ 


LESSON LXIX. 


121. 1. How many yards of cambric which is 3 of 
a yard wide, will be required to line 80 yards of cloth 
that’is 12 yards wide ? 

2. In acertain school } of the pupils study algebra, 
4 geometry, and the mec enee arithmetic ; Ghat per 
eat _ the whole are in each of the studies named ? 

4 less 3, plus 3, multiplied by 14, is how many 
fibica af rf 

4. A dog one night killed 17 sheep, which were 
52 per cent. of a flock; how many of the flock were 
braked " 

5. How many yards of cloth that is 3 of a yard 
wide, are equal to 9 yards that is } of a yard wide? 

6. Joseph earned $11 a day, aed spent $3.50 a 
week for board, and 4 of the remainder of his earn- 
ings for clothes ; at that rate, how much can he save 
in 4 weeks ? 

7. Bought 240 pounds of beef, at 11 cents a pound, 
and sold half of it for 13 cents, and half for 14 cents 
a pound; how much did I gain ? 

8. Bought 25 yards of broadcloth, at $6 per yard, 
and paid for the same in wood, at $7 per cord; how 
much did it take ? 

9. SED Ss being asked his age, replied, if he were 

2 and ¢ older, he should be 40 years old ; how old 
a. he? 

10. Bought 12 buffalo robes, at $12} apiece, and 


133 GENERAL REVIEW. 


paid for them with wood, at $7} a cord; how many 
cords did it take ? 

11. If a frog should be 12 days in getting out of a 
well, by leaping up 12 feet every morning, and falling 
back 4 feet every evening, how deep is the well? 

12. If 25 barrels of agit cost $1314, how much 
will 32 barrels cost ? 

18. What cost % of a hogshead of molasses, at % of 
a dollar a gallon ? 

14. What number increased by 1, by 3, and by } 
of itself, will amount to 39 ? 

15. A and B undertake to travel round a circular 
island 20 miles in circuit, both starting from the same 
point, and going round in the same direction ; when 
A has traveled 19 miles, and B 8, how far apart are 
they ? 

16. Divide $100 among A, B, and C, so that B shall 
have $20 more than A, oa C $15 less than B. 


Norte. — C has $5 more than A, and $100 must be $25 more than 
3 times A’s share. 


LESSON LXX. 


-1. 122. When an article is sold at 2 of its cost, 
what is the loss per cent. ? 

2. What part of the somnep ale is 71 per cent. inter- 
est ? 

3. At what per cent. interest will $10 become $15, 
in 5 years ? 

4. In what time will a given principal double itself, 
at 5} per cent. interest ? 

5. A man can dig a ditch in 3 days, and his son in 
5 days; in what time can they dig it together? 


GENERAL REVIEW. 133 


6. Jason has 25 per cent. more money than Ed- 
ward; what per cent. less has Edward than Jason ? 

7. In how long a time will $60 gain $6.30, at 7 
per cent. interest ? 

8. How much water must be mixed with 10 gal- 
lons of brandy, worth $8 a gallon, that the mixture 
may be worth only $7 a gallon ? 

9. If $100 have been borrowed at 6 per cent. inter- 
est, for 1 year, how long must $250 be loaned at the 
same rate per cent., to requite the favor ? 

10. At what per cent. interest will $30 become $60 
in 123 years? 

11. A lady having a number of peaches, gave away 
1 of them, and 2 of the remainder, and had 27 left ; 
how many had she ? 

12. Four men rent a field for $16; A puts in 6 
cows, B 8 cows, C 4 cows, and D as many cows as 
his paying +, of the rent entitles him to; what part 
of the rent did A, B, and C each pay, and how many 
cows did C put in ? 

13. Sold a watch for $35, and thereby lost 25 per 
cent., when there ought to have been gained 80 per 
cent. ; how much was it sold below its proper value ? 

14. Sold a cart for $30, and thereby lost 20 per 
cent. ; at what price should it have been sold to have 
gained 20 per cent. ? 

15. If 4 horses consume 21 bushels of grain in 6 
jdays, how many bushels will 8 horses consume in 12 
days ? 

16. What per cent. of 50 per cent. of 75 is 25 per 
cent. of 30? 


134 GENERAL REVIEW. 


LESSON LXXI. 

125. 1. The circumference of a circle is 2? nearly 
of its diameter. What then is the circumference of 
a circular garden which is 3 rods in diameter ? 

2. A circular pond is 11 miles in circumference ; 
what is its diameter ? 

3. The area of a circle is equal to half the diam- 
eter multiplied by half the circumference. How 
much greater area has a circle 22 inches in cir- 
cumference, than a square having the same distance 
round it? 

4. If a flagstaff 30 feet in height, at a certain hour, 
casts a shadow of 20 feet, what must be the height 
of that staff which at the same time casts a shadow 
of 25 feet ? 

5. Bought 60 apples at 5 for 9 cents, and sold half 
of them at 2 fora cent, and half at 38 for a cent; 
how much was the gain ? 

6. The sum of two numbers is 19, and twice the 
first added to 5 times the second is 74; what are the 
numbers ? 


Nor. — Twice the first added to twice the second is 38; hence 3 
times the second is 386. 


7. Williams and Brown enter into business to- 
gether; Williams puts in 4 times } of what Brown 
does ; they both put in $1680, and gain $700; what 
is each one’s share of the gain ? 

8. A barrel of flour and a cord of wood cost $17, 
and 2 barrels of flour cost $10 more than a cord of 
wood ; how much does each cost ? 


GENERAL REVIEW. 135 


9. A bought a horse for 25 per cent. less than 
his real value, and sold him to B for 25 per cent. 
more than his value; how much per cent. did A 
make on his purchase? How much per cent. would 
B lose were he to sell the horse for the same price 
that A. gave ? 

10: An apprentice receives from his employer 5 
cents for every good photograph which he produces, 
and forfeits 10 cents for the material consumed in 
every one he spoils; after making 50 attempts he re- 
ceived 1 dollar ; how many did he spoil ? 

11. Two men have a flock of sheep; A has 15 
more than half of the number that B has, and both 
have 54; how many has each ? 

12. Smith and Robinson go into partnership, each 
putting in $300; afterwards Smith puts in twice as 
much, and Robinson 8 times as much, as before; 
what share of the capital has each contributed ? 

13. A hare starts 25 leaps in advance of a hound, 
and takes four leaps to the hound’s 3; but 2 of the 
hound’s leaps equal 3 of the hare’s ; how many leaps 
must the hound take to overtake the hare ? 

14. A has 50 per cent. more property than B, 
and B has 50 per cent. more than C; how much 
per cent. more has A than C? How much per 
cent. less has C than A ? 

15. If a merchant purchases goods for cash to the 
amount of $500, when money is worth 2 per cent.a 
month, what sum will he gain by selling the goods at 
the end of 4 months, but on 3 months’ credit, at an 
advance of 20 per cent. upon the cost? _ 


Al tet NAD TEX 


WRITTEN EXERCISES. 
—9—— 

124. The Exercises here supplied may be used 
at the discretion of the Teacher, as slate or black-board 
drills, in connection with the articles denoted in the 
parentheses. 

(ART. 1—3.) 


125. Write the following figures and read them : — 


(1.) (2.) (3.) (4.) (5.) 
11 10 14 60 18 
13 17 33 29 80 
19 20 40 15 92 
9 23 55 70 44 
16 61 6 83 99 


126. Write the following figures and show what 


. each figure expresses : — 


(1) (2.) (eee) (6) 
121 500 268 645 804 
143 147 100 702 980 


210 302 419 800 999 


APPENDIX. Bus 78 


(ART. 4—6.) 
127, Write in figures and arrange in columns : — 


1. Thirteen, twenty-five, forty-one, thirty-one, fifty- 
eight, fifty. . 

2. Twenty-two, seven, sixteen, fifty-seven, eighty- 
three, seventy-seven. 

3. Twenty-seven, forty-three, ninety-six, eighty- 
eight, ninety-two. 

4, Thirty-nine, one hundred, eleven, three, two 
hundred fifty, six hundred. . 

5. What are ten hundred called? One Thou- 
sand. 


6. Write by figures one thousand. 1000 
Tt. Write by figures one thousand two hundred 
sixty-eight. 1268 


(ART. 7—8.) 
128. Write the following figures and read them :— 


(i) (2.) (3.) (4.) 
1345 2000 5600 9000 
3604 5158 4231 8900 
4172 6250 2503 TT44 
1035 T7000 8088 9999 


(ART. 9—10.) 
129. Write in figures and arrange in columns : — 
1. One thousand seven hundred five, six thousand 
seven hundred ninety-nine, sixty-eight, three thousand 
forty-one. 
2. Four thousand five hundred two, nine thousand 
sixty-six, eight hundred seven, eleven. 


138 APPENDIX. 


3. Eight thousand five hundred thirty-nine, seven 
thousand eight hundred fifteen, six hundred one, 
eighty-six. , 

4. Nine thousand nine hundred seven, eight thou- 
sand, one thousand one hundred twenty-two, three 
hundred three. 

5. Write by figures ten thousand. 10000 

6. Write by figures one hundred thousand. 

| 100000 

7. Write by figures two hundred forty-five thou- 
sand six hundred seventy-five. 245675 

8. In the expression 245,675, how many ones are 
expressed by the three figures at the right of the 
comma? How many thousands by the three figures, 
next at the left ? 

9. What are ten one-hundred thousands called ? 
One Million. 


10. Write by figures one million. 1000000 
11. Write by figures two hundred fifty-eight mill- 
ions. 258000000 


12. In the expression 258000000, what do the third 
three figures from the right express ? 


(ART. 11—13.) 
130. Write the following figures and read them :— 


(1.) -(2.) (3.) _ (4.) 
612451 111000 667009 8887177 
800456 83383 130452 780304 


100000 569248 816721 3140305 
- 222803 472060 82003 . 12999999 


APPENDIX. 139 


151, Write the following figures and arrange in 
columns : — 

1. Six hundred fifteen thousand three hundred 
twenty-two, seven hundred sixty-four thousand seven 
hundred, nine hundred thirty-five, seven hundred, one 
thousand one. 

2. ‘One thousand ninety, one hundred thirteen thou- 
sand one hundred thirteen, four hundred sixty-one 
thousand four hundred twenty-four, three hundred 
seventy-nine thousand two hundred five. 

5. Three hundred nineteen thousand one hundred 
twenty-nine, five hundred thirty thousand one hun- 
dred one, sixty-five million seven hundred thousand 
nine, three hundred thirty-seven thousand five hun- 
dred sixteen. 

4, Three million six hundred thirty-three thousand 
five hundred twenty-three, forty-three million five 
hundred fifty-nine thousand seven hundred sixty-six, 
one hundred eighty-seven million nine hundred seven- 
teen thousand two hundred sixteen, one million one. 


(ART. 14.) 


132. Write 96, 61, 40, 51, and 9 in a column 
and add. 


96 Sotution. — Write the numbers so that the units 
6] shall make the first column, and the tens the second 
40 column. 


5 Wh Begin with the units, add, —9, 10, 11, 17;—— 17 units 
9 are 1 ten and 7 units. 
ee. Write the 7 under the column of units, and add the 1 
257 ten with the tens. 
1, 6, 10, 16, 25, — 25 tens are 2 hundred and 5 tens. 


140 


APPENDIX. 


Write the 5 under the column of tens and the 2 as hundreds. 
The sum is 2 hundreds 5 tens 7 units, or 257. 
To prove the work, add the columns downwards. 


(2.) 
41 
62 
53 


(3.) 
19 
68 
90 
15 


(8.) 
14 
43 


56 


66 
3 


(4,) 
81 
17 
91 

8 


9.) 
12 
85 
18 


22 
40 


(ART. 15—18.) 


183. Write and add:— 


C1.) 
118 
415 
178 
OL 
10 


(2.) 
421 
505 
700 
186 
327 

17 


(7.) 
9605 
104 
39 


eee 


(3.) 


(3-) 
60 
rei 
oT 
25 


(10.) 
49 


18 
. 56 
19 
33 


APPENDIX. 141 


(ART. 19.) 
134. Write and find the sum : — 

(1.) (2.) (3.) (4.) 
41061 16425 S5a00 43201 
70090 52031 4441 62492 

8123 7245 209 57100 

1405 841 apie 41131 


o22 2953S ye ed 2 ee ee ee 


5. What is the sum of 3406, 740, 14, and 11? 
6. What is the sum of 46075, 481, 2016, and 9? 
7. What is the sum of 56415, 4713, 447774, and 
23059 ? 
8. What is the sum of 890881, 46581, 10064, and 
4251? : 
(ART. 20.) 


135. 1. What is the value of 16204 + 15067 + 
21041 + 25333 + 2? 

2. What is the value of 19467 + 17240 + 64810 
+ 30323 + 122? 

3. What is the value of 20003 + 4044 + 77055 + 
9119 + 7? 

4. What is the value of 15063 + 765432 + 10064 
+ 16? 

5. What is the value of 2163 + 16061 + 7481 + 
6050 + 856 ? 

6. Add together four thousand six hundred seventy- 
five, fifteen thousand four hundred fifty-two, one thou- 
sand three hundred eleven, and thirteen thousand 
nine hundred ninety-nine. 


142 APPENDIX. 


7. Find the amount of 1600 dollars, 3095 dollars, 
4519 dollars, and 73 dollars. , 

8. Immigration into this country was 196352 for 
1865, 233418 for 1866, and 242731 for 1867. What 
was the total for the three years ? 

9. The mariner’s compass was discovered 1111 
years before Christ, introduced into Europe 1180 
years after Christ, and 312 years later America was 
discovered. How many years after the discovery of 
the mariner’s compass was the discovery of America ? 

10. The distance from Washington, by railroad, to 
Cincinnati is 509 miles; from Cincinnati to St. Louis 
531 miles; from St. Louis to Fort Kearney 598 miles ;° 
from Fort Kearney to Fort Laramie 450 miles; from 
Fort Laramie to Fort Hall, 526 miles; from Fort 
Hall to Oregon City 762 miles. What is the dis- 
tance from Washington to Oregon City ? 


(ART. 21-24.) 
136. 1: From 627} take 435: 


62'7  Soxrution.— Write the lesser number under the greater, 
436 so that units shall be under units, tens under tens, and 
hundreds under hundreds. 
192 Begin with the units and subtract: 5 units from 7 units 
leave 2 units; write the 2 units under the column of units. 
The 3 tens cannot be taken from 2 tens; but we can take 1 hun- 
dred from the 6 hundreds, leaving 5 hundreds; and the 1 hundred 
taken is 10 tens, which with the 2 tens make 12 tens; 8 tens from 12 
tens leave 9 tens; write the 9 tens under the column of tens. 
4 hundreds from 5 hundreds leave 1 hundred; write the 1 hundred 
under the column of hundreds. 
The difference is 1 hundred 9 tens 2 units, or 192. To prove the 
work add the result found to the number subtracted, and the sum is 
equal to the larger number. Hence the work is presumed to be right. 


(2.) 
From 567 
| Take 456 


(6.) 
From 940 
‘Take 659 


(10.) 
From 100 
Take 37 


(14.) 
From 3104 
Take 1401 


(1.) 
3635 
1534 


ee 


6.) 
6655 
4720 


(9.) 
138402 
4169 


APPENDIX. 
(3.) (4.) 
192 460 
579 274 
(7) ob, 
807 800 
627 99 
(oy (12) 
605 5384 
31 340 
(15.) (16.) 
5060 5060 
4909 59 


(ART. 25-26.) 


(2) 
2521 
1006 


(6.) 


9000 
8 


(10.) 
45609 
10030 


—__——_—— 


137. Write and subtract : — 


(3.) 
6207 
4375 


(7.) 
1446 
374 


(11.) 
78005 
116 


————— 


143 


144 APPENDIX. 


138. From 16045 dollars take 9056 dollars. 

14. Take 64305 tons from 79550 tons. 

15. From nineteen thousand sixteen, subtract one 
thousand, seven hundred eighty-eight. 

16. Find the difference between 86802 and 7085. 

17. Find the difference between 1000 and 999. 

18. Find the difference between one million and 
one thousand one. 

19. What is the value of 89964 — 88352 ? 

20. What is the value of 364020 — 93009 ? 

21. In 1870, there were in the United States 
344596 carpenters, and 141774 blacksmiths. How 
many more were there of the car ponies than of the 
blacksmiths ? 

22. Illinois has an area of 55405 square miles and 
Iowa 50914. How much greater is the area of Ilhi- 
nois than that of Iowa? 

23. How many added to one million ninety-nine 
thousand one hundred twelve will make one million 
five hundred one thousand twenty-nine ? 


(ART. 27.) 


138. 1. A farm cost 4500 dollars and the stock 
upon it 1255 dollars. How much more did the farm 
cost than the stock upon it ? 

2. How much more is 9617 + 1463 than 8671 
a BOY 

3. How much more is 638507 — 6350: than "5908 
+ 6001 + 139 + 18? 

4, A man’s real estate is worth 50675 dollars and 
his personal property 45793 dollars. He owes 


APPENDIX. 145 


46756 dollars ; how much more is his property worth 
than what he owes. 

5. What is the value of 160645 — 84466 + 1100 
+ 9671 + 1903? 

6. What is the value of 33441 + 67009 — 63411 
+ 1169? 

7. In 1870, there were in this country 43874 
clergymen, 62383 physicians and surgeons, and 40736 
lawyers. Required the total of three professions ? 

8. The area of Massachusetts is 7800 square miles, 
of New Hampshire 9280 square miles, and of Ver- 
mont 10,212 square miles. How much do the total 
of these areas come short of 81766 square miles, 
which is the area of Maine? 

9. How much is 38,352 more than 12,656 + 15,000 
+ 13,700 ? | 

10. A merchant bought a car load of flour for 863 
dollars, groceries for 5673 dollars, and paid down 
_ 4975 dollars. How much did he still owe ? 


(ART. 28 — 351.) 
139. Multiply 581 by 6. 


Sotution. Write the 6 under the units’ figure of 
O81 yumber to be multiplied. 
Multiply, thus: 6 times 1 unit are 6 units. Write 

3486 the 6 units for the units of the product. 

6 times 8 tens are 48 tens, which are 4 hundreds and 
8 tens. Write the 8 tens for the tens of the product, and reserve the 
4 hundreds. 

6 times 5 hundreds are 30 hundreds, which with the 4 hundreds 
reserved, or 34 hundreds, are 3 thousands 4 hundreds. Write the 4 
hundreds for the hundreds, and the 3 thousands for the thousands of 
the product. Result, 3486. 

10 


146 APPENDIX. 


(2.) (3.) (4.) (6.) (6.) 
4T5 903 444 960 578 
Soot 8000) 8h, 
(7.) (8.) (9.) (10.) (11.) 
364 (21 406 116 382 
ie ceo 
(12.) (13.) (14) (15.) (16.) 
2112 3004 6203 7118 4125 
T 8 4 6 3 
(17.) (18.) (19.) (20.) (21.) 
6324 13451 3008 65059 76391 
egae 5 T 4 9 
(22.) (23.) (24.) (25.) (26.) 
22402 34004 68223 19091 22089 
6 7 3 6 i) 
(ART. 32.) 


140. 1. Multiply 46138 by 27. 


So.tutTion.— Write the 27 under the number to 
4613. be wultiplied, so that units stand under units and 
2 tens under tens. 
32291 Multiply by the 2 tens, thus: 2 tens are 20 units, 
9226 and 20 times 3 units are 60 units, or 6 tens; write 
—_———— the 6 tens. 20 times 1 ten are 20 tens, or 2 hun- 
1245651 dreds; write the 2 hundreds. 20 times 6 hundreds 
are 120 hundreds, or 1 ten thousand and 2 thous- 
ands; write the 2 thousands, and reserve the 1 ten thousand. 20 
times 4 thousands are 8 ten-thousands, which, with the 1 ten-thous- 
ands reserved, are 9.ten-thousands ; write the 9 ten-thousands; and 
obtain 9226 tens, as a partial product. 
Adding the partial products, obtain as the result, 124551. 


APPENDIX. 


(2.) (3.) (4.) (5.) 
1345 63401 £0064 1312 
_ 40 12 14 8T 

(6.) (7.) (8.) (9.) 
1345 10617 4097 10091 

63 95 8ST 76 
(10.) (11.) (12.) (13.) (14.) 
425 1068 251 T01 641 
125 120 162 1038 231 

(15.) (16.) (17.) (18.) 

3024. 2710 6431 12041 
53 120 39 1038 
(19.) (20.) (21.) (22.) 
12002 1231 8240 70031 

601 73 910 321 

(23.) (24.) (25.) (26.) 
40001 6211 12604 72031 
101 82 321 92 


27. What is the value of 315 x 160? 
28. What is the value of 210 « 210? 
- 29. What is the product of three hundred sixty-five 
multiplied by one hundred ? 
30. What is the weight of 1: cords of maple wood 
at 2878 pounds a cord ? 


148 APPENDIX. 


31. What will it cost to build 80 miles of railroad 
at 22250 dollars a mile? 

32. What is the value of 1805651 acres of land at 
68 dollars per acre ? 


(ART. 33.) 


141. 1. Divide 3486 by 6. 


SoLuTion. — Write the 6 at the ye of the 
6)8486 number to be divided. 
S81 Divide thus: 6 is contained in 34 tun dele 
G °? hundred times with 4 hundreds remaining. 
——— Write the 5 hundreds in the quotient. 
Proof. 3486 The remaining 4 hundreds consider prefixed 
to the 8 tens, making 48 tens. 6 is contained in 
48 tens 8 ten times. Write the 8 tens in the quotient. 
- 6 is contained in 6 units 1 unit times. Write the 1 unit in the 
quotient. 
The result is 5 hundreds, 8 tens, 1 unit, or 581. 
To prove the work, multiply the quotient 581 by 6, the number 
divided by, and obtain 3486, the number which was divided. 


Write and divide : — 


(2.) (3.) (4.) (5.) 
8)3840 8)1832 7)4046 2)1920 
(6.) (7.) (8.) (9.) 
9) 3276 8)5768 5)580 7) 2842 
(10.) (11.) (12.) (13.) 
5)890 9)3438 - 8)28032 424812 
(14.) (15.) (16.) (17.) 
8)12375 2)12648 4) 260238 9687519 


APPENDIX. 149 
(18.) (19.) (20.) (21.) 
6)4500 9) 1530 5)1825 8)7000. 
(22.) (23.) (24.) (25.) 
9)2880 3) 22035 8) 22464 11)98450 
(26.) (27.) (28.) 29.) 
8)18880 11) 9845 6)75012 8)80808 
(30.) (31.) (32.) (33.) 
T)3689 10)67780 11)34831 11)13321 
(34.) (35.) (36.) (37.) 
8)10408 12)11472 = 987809 ~=— 11) 116638 
(ART. 34.) 
142. 1. Divide 1705 by T. 
VI1ITVO5 So.ution. — Dividing, as in Art. 33, we have for 


QABt quotient 243 and a remainder of 4. 
Write the 4 at the right of the quotient with the 7 
under it. Result, 2434. 
To prove the work, multiply the 243 by 7, and to the product add 
the remainder 4, and obtain 1705, the number divided. 


(2.) (3.) (4.) (5.) 
2)1895 3)7805 96000 8)4350 
(6.) (7.) (8) (9.) 
8)13468 — 5)14802 7)90901 9)13400 
10.) (11.) ces (13.) 
8)6834 2)49731 6)1763 8)40324 


| 150 APPENDIX. » 


(14.) 15.) (16) ae 
8)3623 973044 ~=—-10)84660 ©: 12) 84561 


(18.) (19.) (20.) (21.) 
1196345 972341. += 1167890 => 10 8928 
(22.) (23.) (24.) (25.) 
7)11301 8)96350  12)60000 + —-9) 10806 
(26.) Qn) 8) 29.) 


10)73890 12)62815 7)89340 6)81009 


(30.) (31.) (32.) (33.) 
9) LIAdd 10)63011 11)45455 12)60742 


(ART. 35.) 


143. 1. Divide 7886 by 13. 


13)7886(6063; Sorution. — 13 is contained in 78 hundreds, 
V8 6 hundred times. Write the 6 hundreds in the 


86 quotient at the right of the number divided. 
S 13 X 6 = 78, which deducted from the 78 
cCay se: of the dividend giveth no remainder. Bring 


down the next figure. 13 is not contained in 
8, which is tens. Write 0 for the tens in the quotient. Bring down 
the next figure, which with the 8 tens makes 86 units. 13 is con- 
tained in 86 units 6 times with 8 remaining. Write the 6 tens in the 
quotient, and the remainder 8 write with the 13 under it, as a part 
of the quotient. Result, 606 fs: 


(2.) (3.) (4.) (5.) 
1464012 22)12440¢ 8165412 64) 10006 


“APPENDIX. 151 


6. What is the value of 86504 + 25? 

7. What is the value of 10005 + 17? 

8. What is value of 8643 + 100? 

9. What number multiplied by 35 is 7525 ? 

10. What number multiplied by 16 is 19744? 

11. How many acres of land at 47 dollars per acre 
can be bought for 895 dollars ? 

12. How many tons of coal at 7 dollars per ton can 
be bought for 14672 dollars ? 

13. A farm at 18 dollars per acre cost 1908 dollars. 
How many acres did it contain ? 

14. When 63 yards of cloth cost 1575 cents, how 
much is the cloth per yard ? 

15. How many days will it take a vessel sailing 104 
miles a day to go from New York to San Francisco, 
by way of Cape Horn, the distance being 18850 
miles ? 

16. A certain number multiplied by 22 gave as the 
result 8514; what was the number multiplied ? 

17. If the weight of 44 bushels of corn is 2464 
pounds, what is the weight of one bushel ? 

18. When 6972 dollars are paid for 28 acres of 
land, what is the average value per acre? 

19. What is the result of 18000 divided by 16? | 

20. A merchant bought flour at 12 dollars a barrel 
and paid 1932 dollars. How many barrels did he 
buy ? 

21. How many thousand feet of boards at 45 dol- 
lars per thousand can be bought for 20250 dollars ? 

22. When 55 acres of land cost 1875 dollars, how 
much is the land per acre ? 


1 APPENDIX. 


(ART. 36 —87.) 

144, 1. Bought two lots of land, the one contain- 
ing 13 acres and the other 8. How much was the 
cost per acre at $1092 for the whole ? 

2. What is the value of 1092 divided by 13 + 8? 

3. If a railroad train move 651 miles in 21 hours, 
how far will it move in 1 hour ? In 65 hours ? 

4, What is the value of (651 + 21) x 65? 

5. When a man trades 114 barrels of flour at $8 
per barrel for coal at $6 per ton, how many tons of 
coal does he get ? 

6. If 315 be subtracted from 8667, the number 
obtained will be how many times 32? 

7. How many acres of land at $55 per acre can be 
bought for $9640, and how many dollars will remain ? 

8. When $495 are pai. for 45 barrels of flour, how 
much is the cost per barrel? How much the cost of 
42 barrels ? | 

9. When the cost of 6 houses is $12600, how much 
is the cost of 1 house? How much is the cost of 18 
houses ? 

10. What is the value of (1655 x 110) + 55? 

11. Paid for 35 sheep $175; what will 123 cost at 
the same rate ? 

12. A farmer raised 9675 bushels of wheat averag- 
ing 43 bushels per acre sown. How many acres had 
he sown’?. What was the yield for a farm of 160 
acres ? 


ie 


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